# Common Core: Building Functions

##### HSF.BF.A2

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

October 1, 2018
##### HSF.BF.B3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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 … Read More “HSF.BF.B3”

October 1, 2018
##### HSF.BF.B4

Find inverse functions.

October 1, 2018
##### HSF.BF.B4a

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) = 2 x³ or f(x) = (x+1)/(x-1) for x ≠ 1.

October 1, 2018
##### HSF.BF.B4b

(+) Verify by composition that one function is the inverse of another.

October 1, 2018
##### HSF.BF.B4c

(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.

October 1, 2018
##### HSF.BF.B4d

(+) Produce an invertible function from a non-invertible function by restricting the domain.

October 1, 2018
##### HSF.BF.B5

(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

October 1, 2018
##### HSF.BF.A1c

(+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

October 1, 2018
##### HSF.BF.A1

Write a function that describes a relationship between two quantities.*

October 1, 2018
##### HSF.BF.A1a

Determine an explicit expression, a recursive process, or steps for calculation from a context.

October 1, 2018
##### HSF.BF.A1b

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.

October 1, 2018