Search the California Content Standards

Cluster:
Build a function that models a relationship between two quantities. [Quadratic and exponential]

Standard:
Write a function that describes a relationship between two quantities. * Determine an explicit expression, a recursive process, or steps for calculation from a context. *

Cluster:
Build a function that models a relationship between two quantities. [Quadratic and exponential]

Standard:
Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. *

Cluster:
Build new functions from existing functions. [Quadratic, absolute value]

Standard:
Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Cluster:
Build new functions from existing functions. [Quadratic, absolute value]

Standard:
Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x^3.

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:
Understand similarity in terms of similarity transformations.

Standard:
Verify experimentally the properties of dilations given by a center and a scale factor: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

Cluster:
Understand similarity in terms of similarity transformations.

Standard:
Verify experimentally the properties of dilations given by a center and a scale factor: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Cluster:
Understand similarity in terms of similarity transformations.

Standard:
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Cluster:
Understand similarity in terms of similarity transformations.

Standard:
Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.

Cluster:
Prove theorems involving similarity. [Focus on validity of underlying reasoning while using variety of formats.]

Standard:
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally and conversely; the Pythagorean Theorem proved using triangle similarity.