Search the California Content Standards

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:
Create equations that describe numbers or relationships.

Standard:
Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA *

Cluster:
Create equations that describe numbers or relationships.

Standard:
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. *

Cluster:
Create equations that describe numbers or relationships.

Standard:
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. * [Include formulas involving quadratic terms.]

Cluster:
Interpret functions that arise in applications in terms of the context. [Quadratic]

Standard:
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. *

Cluster:
Interpret functions that arise in applications in terms of the context. [Quadratic]

Standard:
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *

Cluster:
Interpret functions that arise in applications in terms of the context. [Quadratic]

Standard:
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. *