# Guide to Parent Functions Teenage Girl Sits Smiling at a Desk in Front of a Blackboard. Digital Vision/Getty Images

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.

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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)
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• Equation: y = x2
• 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)
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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)
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## Exponential Growth Parent Function

• Equation: y = bx(where |b| > 0)
• Domain: All real numbers
• Range: All real numbers greater than or equal to 0. (y ≥ 0)
• Y-intercept: (0,1)
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## Exponential Decay Parent Function

• Equation: y = bx
• Domain: All real numbers
• Range: All real numbers greater than or equal to 0. (y ≥ 0)
• Y-intercept: (0,1)
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## Sine Parent Function

• Equation: y = sin
• Domain: All real numbers
• Range: All real numbers between -1 and 1 (-1≤ y ≤ 1)
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## Cosine Parent Function

• Equation: y = cosx
• Domain: All real numbers
• Range: All real numbers between -1 and 1 (-1≤ y ≤ 1)
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## Tangent Parent Function

• Equation: y = tanx