### 4: Building Functions

#### 4.1: Write a function that describes a relationship between two quantities.

4.1.1: Combine functions using the operations addition, subtraction, multiplication, and division to build new functions that describe the relationship between two quantities in mathematical and real-world situations.

#### 4.3: Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x)=y and g(y)=x, for all values of x in the domain of f and all values of y in the domain of g, and find inverse functions for one-to-one function or by restricting the domain.

4.3.2: If a function has an inverse, find values of the inverse function from a graph or table.

### 5: Interpreting Functions

#### 5.4: Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases.

5.4.4: Graph trigonometric functions, showing period, midline, and amplitude.

### 7: Trigonometry

#### 7.2: Define sine and cosine as functions of the radian measure of an angle in terms of the x - and y - coordinates of the point on the unit circle corresponding to that angle and explain how these definitions are extensions of the right triangle definitions.

7.2.1: Define the tangent, cotangent, secant, and cosecant functions as ratios involving sine and cosine.

7.2.2: Write cotangent, secant, and cosecant functions as the reciprocals of tangent, cosine, and sine, respectively.

### 12: Vector and Matrix Quantities

#### 12.4: Perform operations on vectors.

12.4.1: Add and subtract vectors using components of the vectors and graphically.

12.4.2: Given the magnitude and direction of two vectors, determine the magnitude of their sum and of their difference.

#### 12.11: Apply 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

Correlation last revised: 1/5/2017

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