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PARENT FUNCTIONS Constant Function Inverse Linear (Identity)Inverse Squared Absolute Value Exponential Quadratic Logarithmic Cubic Sine Square Root Cosine SignumGreatest Integer

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Constant FunctionInverse or Rational Linear (Identity)Inverse Squared Absolute ValueExponential QuadraticLogarithmic CubicSine Square RootSquare Root CosineCosine SignumGreatest Integer Parent Functions Menu 1) Click on this Button to View All of the Parent Functions. or 2) Click on a Specific Function Below for the Properties. 3) Use the button to return to this menu.

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Constant Function f(x) = a where a = any #

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Constant Function Domain: Range: Parent Equation: f(x) = 2

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Constant Function Parent Equation: f(x) = 2 x – intercept: y – intercept: None

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Constant Function Graph Description: Horizontal Line Table: xy -22 2 02 12 22 Parent Equation: f(x) = 2

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Linear Function (Identity) f(x) = x

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Linear Function (Identity) Domain: Range: Parent Equation: f(x) = x

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Linear Function (Identity) Parent Equation: f(x) = x x – intercept: y – intercept:

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Linear Function (Identity) Parent Equation: f(x) = x Table: xy -2 00 11 22 Graph Description: Diagonal Line

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Absolute Value Function f(x) = x

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Absolute Value Function Domain: Range: Parent Equation: f(x) = x

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Absolute Value Function Parent Equation: f(x) = x x – intercept: y – intercept:

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Absolute Value Function Table: xy -22 1 00 11 22 Parent Equation: Graph Description: V - shaped f(x) = x

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f(x) = x 2 Quadratic Function

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f(x) = x 2 Quadratic Function Domain: Range: Parent Equation:

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Quadratic Function Parent Equation: x – intercept: y – intercept: f(x) = x 2

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Quadratic Function Table: xy -24 1 00 11 24 Parent Equation: Graph Description: U - shaped

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Cubic Function f(x) = x 3

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Cubic Function f(x) = x 3 Domain: Range: Parent Equation:

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Cubic Function f(x) = x 3 Parent Equation: x – intercept: y – intercept:

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Cubic Function f(x) = x 3 Parent Equation: Table: xy -2-8 00 11 28 Graph Description: Squiggle, Swivel

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f(x) = x Square Root Function

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f(x) = x Square Root Function Domain: Range: Parent Equation:

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f(x) = x Square Root Function Parent Equation: x – intercept: y – intercept:

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f(x) = x Square Root Function Parent Equation: Table: xy 00 11 42 93 164 Graph Description: Horizontal ½ of a Parabola

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f(x) = 1 x Inverse Function or Rational Function (Reciprocal of x)

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f(x) = 1 x Inverse Function or Rational Function (Reciprocal of x) Parent Equation: Domain: Range:

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f(x) = 1 x Inverse Function or Rational Function (Reciprocal of x) Parent Equation: x – intercept: y – intercept:

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Inverse Function or Rational Function (Reciprocal of x) Table: xy -2-0.5 0Error 11 20.5 f(x) = 1 x Parent Equation: Graph Description: Opposite L Curves in 1 st and 3 rd Quadrants

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Inverse Squared Function (Reciprocal of x 2 ) f(x) = 1 x 2x 2

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Inverse Squared Function (Reciprocal of x 2 ) f(x) = 1 x 2x 2 Parent Equation: Domain: Range:

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Inverse Squared Function (Reciprocal of x 2 ) f(x) = 1 x 2x 2 x – intercept: y – intercept: Parent Equation:

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Inverse Squared Function (Reciprocal of x 2 ) f(x) = 1 x 2x 2 Parent Equation: Table: xy -20.25 1 0Error 11 20.25 Graph Description: Symmetrical L Curves in 1 st and 2 nd Quadrants

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Exponential Function b = base and x = exponent

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f(x) = 2 x Exponential Function Domain: Range: Parent Equation:

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f(x) = 2 x Exponential Function x – intercept: y – intercept: Parent Equation:

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f(x) = 2 x Exponential Function Table: xy -20.25 0.5 01 12 24 Parent Equation: Graph Description: Backwards L Curves

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f(x) = log x Logarithmic Function

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f(x) = log x Logarithmic Function Range: Parent Equation: Domain:

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f(x) = log x Logarithmic Function x – intercept: y – intercept: Parent Equation:

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Logarithmic Function Table: xy -2Error Error 0 10 20.301 Parent Equation: Graph Description: Upside Down L curve in 1 st and 4 th Quadrant f(x) = log x

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Step Function (Greatest Integer) f(x) = [x]

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Step Function (Greatest Integer) f(x) = [x] Domain: Range: Parent Equation:

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Step Function (Greatest Integer) f(x) = [x] Parent Equation: x – intercept: y – intercept:

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Step Function (Greatest Integer) f(x) = [x] Parent Equation: Graph Description: Stair Steps Table: xy -2 00 11 22

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Signum Function

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Domain: Range: Parent Equation:

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Signum Function Parent Equation: x – intercept: y – intercept:

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Signum Function Table: xy -2 00 11 21 Parent Equation: Graph Description: Left and Right Arrows Opposite Directions

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Sine Function f(x) = sin x

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Sine Function f(x) = sin x Domain: Range: Parent Equation:

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Sine Function f(x) = sin x x – intercept: y – intercept: Parent Equation:

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Sine Function f(x) = sin x Table: xy -2-0.9093 -0.8415 00 10.8415 20.9093 Parent Equation: Graph Description: Wavy, above and below x-axis with y-int at (0, 0)

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Cosine Function f(x) = cos x

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Cosine Function f(x) = cos x Domain: Range: Parent Equation:

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Cosine Function f(x) = cos x x – intercept: y – intercept:

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Cosine Function f(x) = cos x Table: xy -2-0.4161 0.5403 01 1 2-0.4161 Parent Equation: Graph Description: Wavy, above and below x-axis with y-int at (0, 1)

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