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### Guide to Parent Functions

The modern dating game is a staple of reality TV. *For the Love of Ray J*, *Flavor of Love*, and *The Bachelorette* all descend from the same daddy: *The Bachelor*. Although some of *The Bachelor's* derivative shows differ, they all take cues from *The Bachelor.*

### Dating Show Characteristics

- 1 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.

### Types of Functions

- Linear
- Quadratic
- Absolute Value
- Exponential Growth
- Exponential Decay
- Trigonometric (Sine, Cosine, Tangent)
- Rational
- Exponential
- Square Root

Each of these functions has a parent function. This article focuses on the traits of the parent functions.

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### Linear Parent Function

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

### Additional Information about Linear Functions

- Changes in the Parent Function
- Slope of a Line

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### 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)*x*-intercept: (0,0)- Line of symmetry: (x = 0)
- Vertex: (0,0)

### Additional Information about Quadratic Functions

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### 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)

### Additional Information about Absolute Value Functions

Definition of Absolute Value

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### Exponential Growth Parent Function

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

### Additional Information about Exponential Growth Functions

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### Exponential Decay Parent Function

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

### Additional Information about Exponential Decay Functions

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### Sine Parent Function

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

### Additional Information about Sine Functions

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### Cosine Parent Function

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