Search the California Content Standards

Cluster:
Define, evaluate, and compare functions.

Standard:
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Footnote:
Function notation is not required in grade 8.

Cluster:
Define, evaluate, and compare functions.

Standard:
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Cluster:
Define, evaluate, and compare functions.

Standard:
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Cluster:
Use functions to model relationships between quantities.

Standard:
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Cluster:
Use functions to model relationships between quantities.

Standard:
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Cluster:
Prove and apply trigonometric identities.

Standard:
Prove the Pythagorean identity sin^2(θ ) + cos^2(θ ) = 1 and use it to find sin(θ ), cos(θ ), or tan(θ ) given sin(θ ), cos(θ ), or tan(θ ) and the quadrant of the angle.

Cluster:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Cluster:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Cluster:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Cluster:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.