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 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. [For F.BF.1, 2, linear, exponential, and quadratic]

Standard:
Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. *

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 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:
Understand the concept of a function and use function notation. [Learn as general principle; focus on linear and exponential and on arithmetic and geometric sequences.]

Standard:
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Cluster:
Understand the concept of a function and use function notation. [Learn as general principle; focus on linear and exponential and on arithmetic and geometric sequences.]

Standard:
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Cluster:
Understand the concept of a function and use function notation. [Learn as general principle; focus on linear and exponential and on arithmetic and geometric sequences.]

Standard:
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n − 1) for n ≥ 1.

Cluster:
Interpret functions that arise in applications in terms of the context. [Linear, exponential, and 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. [Linear, exponential, and quadratic]

Standard:
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*