#### Vocab

Domain – the span of all the x-values of a function

Range – the span of all the y-values of a function

x-intercept(s) – the point(s) where a function touches the x-axis

y-intercept – the point where a function touches the y-axis

Horizontal asymptote(s) – the imaginary line(s) where the domain of a rational function approaches on both sides but never touches.

- There are three rules that define where the asymptote will be and how it will look like:
- If the degree of the numerator is less than the degree of the denominator, the asymptote will, by default, be y = 0.
- The asymptote will be higher or lower if there is a k value in the function.

- If the degree of the numerator is equal to the degree of the denominator, the asymptote will, by default, be at y = (degree of the numerator/degree of the denominator)
- The asymptote will be higher or lower if there is a k value in the function.

- If the degree of the numerator is greater than the degree of the denominator, there will not be a horizontal asymptote.

- If the degree of the numerator is less than the degree of the denominator, the asymptote will, by default, be y = 0.

Vertical asymptote – the imaginary line(s) where the range of a rational function approaches above and below but never touches.

Local minimum – the point where a positive even polynomial’s vertex is, where the function does not go any lower.

Local maximum – the point where a negative even polynomial’s vertex is, where the function does not go any higher.

End behavior – the direction, attributes, and/or limit of a function as it goes left or right.

#### Linear

#### Quadratic

#### Rational Function

#### Radical Function

#### Rational Function

#### Radical Function

#### Application

The height of a passenger on an escalator is modeled as

where * t* is the time in seconds after the passenger has boarded the escalator on the second floor and

*is the height in feet above the first floor.*

**h**This means it takes the passenger **16 seconds** to reach the first floor (0 feet).

This means the passenger is **12 feet** above the first floor when he/she first gets on the escalator. Likewise, this also means that the second floor is 12 feet above the first floor.

#### Inverse Functions

Find the inverse of the following function:

#### Composition of Functions

Find f(g(x)) and its domain if:

and:

#### Decomposition of Functions

Find what h(x) decomposes into if:

and: