The modern dating game is a staple of reality TV. "The Bachelorette" and "Flavor of Love," for example, both descended from the same parent: "The Bachelor." Although these shows may differ slightly from "The Bachelor," they still share major characteristics with the parent show:

- There is one attractive person for several potential suitors.
- The show will conclude with matching true loves.
- Backbiting is involved.

Similarly, each family of algebraic functions is headed by a parent, as described in the following sections, including example equations.

01

of 09

## Types of Functions

- Linear
- Quadratic
- Absolute value
- Exponential growth
- Exponential decay
- Trigonometric (sine, cosine, tangent)
- Rational
- Exponential
- Square root

02

of 09

## Linear Parent Function

- Equation: y = x
- Domain: All real numbers
- Range: All real numbers
- Slope of the line:
*m*= 1 - Y-intercept: (0,0)

03

of 09

## Quadratic Parent Function

- Equation: y = x
^{2} - Domain: All real numbers
- Range: All real numbers greater than or equal to 0. (y ≥ 0)
- Y-intercept: (0,0)
- S-intercept: (0,0)
- Line of symmetry: (x = 0)
- Vertex: (0,0)

04

of 09

## Absolute Value Parent Function

- Equation: y = |
*x|* - Domain: All real numbers
- Range: All real numbers greater than or equal to 0. (y ≥ 0)
- Y-intercept: (0,0)
- X-intercept: (0,0)
- Line of symmetry: (x = 0)
- Vertex: (0,0)

05

of 09

## Exponential Growth Parent Function

- Equation: y = b
^{x}(where |b| > 0) - Domain: All real numbers
- Range: All real numbers greater than or equal to 0. (y ≥ 0)
- Y-intercept: (0,1)

06

of 09

## Exponential Decay Parent Function

- Equation: y = b
^{x} - Domain: All real numbers
- Range: All real numbers greater than or equal to 0. (y ≥ 0)
- Y-intercept: (0,1)

07

of 09

## Sine Parent Function

- Equation: y = sin
- Domain: All real numbers
- Range: All real numbers between -1 and 1 (-1≤ y ≤ 1)

08

of 09

## Cosine Parent Function

- Equation: y = cosx
- Domain: All real numbers
- Range: All real numbers between -1 and 1 (-1≤ y ≤ 1)

09

of 09

## Tangent Parent Function

- Equation: y = tanx