Unit 3: Composite and Inverse Functions

Flashcards for composite and inverse functions, covering shifting, reflecting, and scaling, and inverse functions.

Shifting Functions

Involves rep(x - h) and graphed with opposites along the axis. g(x) = f(x - hor shift) + k

Reflecting Functions

Making g(x) ___ f(x). Horizontal ___ over the y-axis if x is affected. Vertical ___ over the x-axis if the coefficient is affected.

Scaling Functions

Deals with _______ vertically and horizontally. Vertical: kf(x), Horizontal: f(kx)

Vertical Scaling

If the coefficient multiplies by the function, you _______. It does not affect AOS and x-intercept but can affect constant and y-intercept.

Horizontal Scaling

If the coefficient multiplies with the variable in the function, you ________. It does not affect the constant or y-intercept but affects AOS and x-intercept.

Function Transformations

g(x) = f(x) + k (vertical shift), g(x) = f(x - k) (horizontal shift), g(x) = -f(x) (reflect vertical), g(x) scaled down by a fraction coefficient, g(x) reflected due to negative

Horizontal Shift

f(x) = (x - h) + k, where h = _____

Vertical Shift

f(x) = (x - h) + k, where k = ____

Domain

A set of all inputs over which the function has defined outputs.

Range

The set of all possible outputs from where the function has defined inputs.

Interval Notation

Uses open and closed intervals to describe sets of numbers. Closed interval uses brackets [ ], open interval uses parentheses ( ).

Inverse Functions

Solve in terms of the other variable. x and y values SWAP in ____.

Inverse Function Graphing

In graphing terms, f(a) = b, then f⁻¹(b) = a. _____ uses a reflection across y = x.