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  • South Carolina Standards
  • Mathematics: Algebra 2 with Probability

South Carolina - Mathematics: Algebra 2 with Probability

2025 College- and Career-Ready Standards | Adopted: 2023

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

A2P.MPS: : Mathematical Process Standards


A2P.MPS.PS: : PROBLEM SOLVING

A2P.MPS.PS.1: : Make sense of problems and persevere in solving them strategically.

Screenshot of Cat and Mouse (Modeling with Linear Systems)

Cat and Mouse (Modeling with Linear Systems)

Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview


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Screenshot of Cat and Mouse (Modeling with Linear Systems) - Metric

Cat and Mouse (Modeling with Linear Systems) - Metric

Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview


Lesson Info
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Screenshot of Estimating Population Size

Estimating Population Size

Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview


Lesson Info
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Screenshot of Real-Time Histogram

Real-Time Histogram

Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected. 5 Minute Preview


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Screenshot of Trends in Scatter Plots

Trends in Scatter Plots

Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview


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A2P.MPS.RC: : REPRESENTATION & COMMUNICATION

A2P.MPS.RC.1: : Explain ideas using precise and contextually appropriate mathematical language, tools, and models.

Screenshot of Biconditional Statements

Biconditional Statements

Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form. 5 Minute Preview


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Screenshot of Conditional Statements

Conditional Statements

Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form. 5 Minute Preview


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Screenshot of Geometric Probability

Geometric Probability

Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview


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Screenshot of Linear Programming

Linear Programming

Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response. 5 Minute Preview


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Screenshot of Sight vs. Sound Reactions

Sight vs. Sound Reactions

Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user. 5 Minute Preview


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A2P.MPS.C: : CONNECTIONS

A2P.MPS.C.1: : Demonstrate a deep and flexible conceptual understanding of mathematical ideas, operations, and relationships while making real-world connections.

Screenshot of Cat and Mouse (Modeling with Linear Systems)

Cat and Mouse (Modeling with Linear Systems)

Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Cat and Mouse (Modeling with Linear Systems) - Metric

Cat and Mouse (Modeling with Linear Systems) - Metric

Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Compound Interest

Compound Interest

Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview


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Screenshot of Exponential Growth and Decay

Exponential Growth and Decay

Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview


Lesson Info
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Screenshot of Linear Programming

Linear Programming

Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response. 5 Minute Preview


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A2P.MPS.AJ: : ANALYZE & JUSTIFY

A2P.MPS.AJ.1: : Use critical thinking skills to reason both abstractly and quantitatively.

Screenshot of Estimating Population Size

Estimating Population Size

Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Linear Programming

Linear Programming

Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Percent of Change

Percent of Change

Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview


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Screenshot of Permutations and Combinations

Permutations and Combinations

Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview


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A2P.MPS.SP: : STRUCTURE & PATTERNS

A2P.MPS.SP.1: : Identify and apply regularity in repeated reasoning to make generalizations.

Screenshot of Compound Interest

Compound Interest

Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview


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Screenshot of Exponential Growth and Decay

Exponential Growth and Decay

Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview


Lesson Info
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Screenshot of Finding Patterns

Finding Patterns

Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid. 5 Minute Preview


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Screenshot of Pattern Finder

Pattern Finder

Observe frogs jumping around on colored lily pads. Find, test, and reason about patterns you see in their jumping. 5 Minute Preview


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A2P.DPSR: : Data, Probability, and Statistical Reasoning


A2P.DPSR.1: : Understand independence and conditional probability and use them to interpret data.

A2P.DPSR.1.2: : Explain whether two events, A and B, are independent if and only if the probability of A and B occurring together is the product of their probabilities and use this characterization to determine if they are independent.

Screenshot of Independent and Dependent Events

Independent and Dependent Events

Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview


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A2P.DPSR.1.3: : Determine whether the conditional probability of A given B as P(A and B)/P(B) and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B in mathematical and real-world situations.

Screenshot of Independent and Dependent Events

Independent and Dependent Events

Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview


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A2P.DPSR.1.4: : Recognize and explain the concepts of conditional probability and independence.

Screenshot of Independent and Dependent Events

Independent and Dependent Events

Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview


Lesson Info
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A2P.DPSR.2: : Use the rules of probability to compute probabilities of compound events in a uniform probability model.

A2P.DPSR.2.1: : Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A and interpret the answer in terms of the model.

Screenshot of Independent and Dependent Events

Independent and Dependent Events

Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview


Lesson Info
Launch Gizmo

A2P.DPSR.2.3: : Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A) x P(B|A) = P(B) x P(A|B) and interpret the answer in terms of the model.

Screenshot of Independent and Dependent Events

Independent and Dependent Events

Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview


Lesson Info
Launch Gizmo

A2P.DPSR.2.4: : Use permutations and combinations to determine the number of possible outcomes in a sample space.

Screenshot of Permutations and Combinations

Permutations and Combinations

Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview


Lesson Info
Launch Gizmo

A2P.MGSR: : Measurement, Geometry, and Spatial Reasoning


A2P.MGSR.1: : Explore and analyze sine and cosine functions using the unit circle, right triangle definitions, and models of periodic phenomena.

A2P.MGSR.1.1: : Build the unit circle for sine and cosine functions using right triangle definitions.

Screenshot of Cosine Function

Cosine Function

Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview


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Screenshot of Sine Function

Sine Function

Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview


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A2P.MGSR.1.2: : Use models of periodic phenomena to evaluate and analyze the graph of sine and cosine functions.

Screenshot of Cosine Function

Cosine Function

Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview


Lesson Info
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Screenshot of Sine Function

Sine Function

Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview


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A2P.NR: : Numerical Reasoning


A2P.NR.1: : Recognize that the complex number system extends the real number system to allow for solution to all polynomial equations.

A2P.NR.1.1: : Understand that there is an imaginary unit i such that i² = -1 and explain the structure of a complex number as a + bi, where a and b are real.

Screenshot of Points in the Complex Plane

Points in the Complex Plane

Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview


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Screenshot of Roots of a Quadratic

Roots of a Quadratic

Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview


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A2P.NR.1.2: : Add, subtract, and multiply complex numbers.

Screenshot of Points in the Complex Plane

Points in the Complex Plane

Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview


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A2P.NR.2: : Represent and manipulate data using matrices.

A2P.NR.2.1: : Perform operations with matrices including addition, subtraction, and scalar multiplication.

Screenshot of Dilations

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form. 5 Minute Preview


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Screenshot of Translations

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview


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A2P.PAFR: : Patterns, Algebra, and Functional Reasoning


A2P.PAFR.1: : Explore and analyze quadratic and polynomial functions and inequalities and use them to model real-world situations.

A2P.PAFR.1.1: : Graph, identify roots, and analyze quadratic functions in mathematical and real-world situations.

Screenshot of Quadratics in Factored Form

Quadratics in Factored Form

Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview


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Screenshot of Quadratics in Polynomial Form

Quadratics in Polynomial Form

Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview


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Screenshot of Quadratics in Vertex Form

Quadratics in Vertex Form

Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview


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Screenshot of Roots of a Quadratic

Roots of a Quadratic

Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview


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Screenshot of Zap It! Game

Zap It! Game

Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview


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A2P.PAFR.1.2: : Solve quadratic inequalities that model mathematical and real-world situations.

Screenshot of Quadratic Inequalities

Quadratic Inequalities

Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response. 5 Minute Preview


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A2P.PAFR.1.3: : Graph and analyze polynomial functions in mathematical and real-world situations.

Screenshot of Graphs of Polynomial Functions

Graphs of Polynomial Functions

Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview


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Screenshot of Polynomials and Linear Factors

Polynomials and Linear Factors

Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview


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A2P.PAFR.1.5: : Recognize perfect squares and perfect cubes and use them to describe the structure of polynomials.

Screenshot of Graphs of Polynomial Functions

Graphs of Polynomial Functions

Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview


Lesson Info
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Screenshot of Polynomials and Linear Factors

Polynomials and Linear Factors

Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview


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A2P.PAFR.2: : Explore and analyze rational and radical functions and use them to model real-world phenomena.

A2P.PAFR.2.1: : Graph rational and radical functions and describe their key features. Limit to square roots and cube roots only.

Screenshot of Direct and Inverse Variation

Direct and Inverse Variation

Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview


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Screenshot of General Form of a Rational Function

General Form of a Rational Function

Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview


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Screenshot of Radical Functions

Radical Functions

Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview


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Screenshot of Rational Functions

Rational Functions

Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview


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A2P.PAFR.2.3: : Create and solve rational and radical equations in one variable, including those that model real-life situations, and verify solutions to identify extraneous solutions if they appear.

Screenshot of Radical Functions

Radical Functions

Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview


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A2P.PAFR.3: : Explore and analyze exponential functions and use them to model real-world phenomena.

A2P.PAFR.3.1: : Create, solve, and graph exponential functions, including those that model real-life situations.

Screenshot of Exponential Functions

Exponential Functions

Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview


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Screenshot of Exponential Growth and Decay

Exponential Growth and Decay

Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview


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Screenshot of Introduction to Exponential Functions

Introduction to Exponential Functions

Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview


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A2P.PAFR.4: : Reason with parent functions to find families of functions that all have similar distinguishing attributes common to the family and use common characteristics to aid in rewriting and identifying functions.

A2P.PAFR.4.1: : Identify the effect on the graph of replacing f(x) by kf(x), f(x) + k, f(kx) for any real number k including multiple transformations; write an equation of a transformed parent function given its graph. Extend to equations involving rational, polynomial, radical, exponential, and piecewise.

Screenshot of Absolute Value with Linear Functions

Absolute Value with Linear Functions

Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview


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Screenshot of Exponential Functions

Exponential Functions

Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview


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Screenshot of Graphs of Polynomial Functions

Graphs of Polynomial Functions

Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview


Lesson Info
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Screenshot of Introduction to Exponential Functions

Introduction to Exponential Functions

Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview


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Screenshot of Radical Functions

Radical Functions

Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Rational Functions

Rational Functions

Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview


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A2P.PAFR.5: : Explore and analyze piecewise functions and linear absolute value inequalities and use them to model real-world phenomena.

A2P.PAFR.5.1: : Graph piecewise functions and describe their key features.

Screenshot of Absolute Value with Linear Functions

Absolute Value with Linear Functions

Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview


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A2P.PAFR.5.2: : Solve linear absolute value inequalities.

Screenshot of Absolute Value Equations and Inequalities

Absolute Value Equations and Inequalities

Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview


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A2P.PAFR.6: : Represent and interpret functions symbolically and graphically.

A2P.PAFR.6.1: : Find the inverse of functions and verify graphically.

Screenshot of Logarithmic Functions

Logarithmic Functions

Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview


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A2P.PAFR.6.3: : Use linear programming to solve systems of equations and inequalities by addressing the constraints that arise in real-world situations.

Screenshot of Linear Programming

Linear Programming

Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response. 5 Minute Preview


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Correlation last revised: 8/22/2024

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