Search the California Content Standards

Cluster:
Build a function that models a relationship between two quantities. [For F.BF.1, 2, linear, exponential, and quadratic]

Standard:
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. *

Cluster:
Build a function that models a relationship between two quantities. [For F.BF.1, 2, linear and exponential (integer inputs)]

Standard:
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. *

Cluster:
Build new functions from existing functions. [Linear and exponential; focus on vertical translations for exponential.]

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. [Linear, exponential, quadratic, and absolute value; for F.BF.4a, linear only]

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. [Linear, exponential, quadratic, and absolute value; for F.BF.4a, linear only]

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.

Cluster:
Experiment with transformations in the plane.

Standard:
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Cluster:
Make geometric constructions. [Formalize and explain processes.]

Standard:
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Cluster:
Make geometric constructions. [Formalize and explain processes.]

Standard:
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Cluster:
Experiment with transformations in the plane.

Standard:
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

Cluster:
Experiment with transformations in the plane.

Standard:
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.