Search the California Content Standards

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

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 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 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:
Interpret the structure of expressions. [Quadratic and exponential]

Standard:
Interpret expressions that represent a quantity in terms of its context. * Interpret parts of an expression, such as terms, factors, and coefficients. *

Cluster:
Interpret the structure of expressions. [Quadratic and exponential]

Standard:
Interpret expressions that represent a quantity in terms of its context. * Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)^n as the product of P and a factor not depending on P. *

Cluster:
Interpret the structure of expressions. [Quadratic and exponential]

Standard:
Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 – (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^2)(x^2 + y^2).