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**PARENT FUNCTIONS Constant Function Inverse**

Linear (Identity) Inverse Squared Absolute Value Exponential Quadratic Logarithmic Cubic Sine Square Root Cosine Signum Greatest Integer

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**Parent Functions Menu Constant Function Inverse or Rational**

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. Constant Function Inverse or Rational Linear (Identity) Inverse Squared Absolute Value Exponential Quadratic Logarithmic Cubic Sine Square Root Cosine Signum Greatest Integer

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

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

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**Table: x y -2 2 -1 1 Parent Equation: f(x) = 2**

Constant Function Table: x y -2 2 -1 1 Parent Equation: f(x) = 2 Graph Description: Horizontal Line

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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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**y – intercept: x – intercept: Parent Equation: f(x) = x**

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

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**Parent Equation: f(x) = x**

Linear Function (Identity) Table: x y -2 -1 1 2 Parent Equation: f(x) = x Graph Description: Diagonal Line

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Absolute Value Function f(x) = │x │

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

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**y – intercept: x – intercept: Parent Equation: f(x) = │x │**

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

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**Table: x y -2 2 -1 1 Parent Equation: Graph Description: “V” - shaped**

Absolute Value Function Table: x y -2 2 -1 1 Parent Equation: f(x) = │x │ Graph Description: “V” - shaped

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Quadratic Function f(x) = x 2

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

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**y – intercept: x – intercept: Parent Equation: Quadratic Function**

f(x) = x 2

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**Table: x y -2 4 -1 1 2 Parent Equation:**

Quadratic Function Table: x y -2 4 -1 1 2 Parent Equation: f(x) = x 2 Graph Description: “U” - shaped

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Cubic Function f(x) = x 3

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

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**y – intercept: x – intercept: Parent Equation: Cubic Function**

f(x) = x 3

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**Table: x y -2 -8 -1 1 2 8 Parent Equation:**

Cubic Function Table: x y -2 -8 -1 1 2 8 Parent Equation: f(x) = x 3 Graph Description: Squiggle, Swivel

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Square Root Function f(x) = x

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

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**y – intercept: x – intercept: Parent Equation: Square Root Function**

f(x) = x

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**Table: x y 1 4 2 9 3 16 Parent Equation: Square Root Function f(x) = x**

1 4 2 9 3 16 Parent Equation: f(x) = x Graph Description: Horizontal ½ of a Parabola

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**Inverse Function or Rational Function**

(Reciprocal of x) f(x) = 1 x

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**Inverse Function or Rational Function**

(Reciprocal of x) f(x) = 1 x Parent Equation: Domain: Range:

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**Inverse Function or Rational Function**

(Reciprocal of x) f(x) = 1 x Parent Equation: x – intercept: y – intercept:

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**Inverse Function or Rational Function**

(Reciprocal of x) Table: x y -2 -0.5 -1 Error 1 2 0.5 f(x) = 1 x Parent Equation: Graph Description: Opposite “L” Curves in 1st and 3rd Quadrants

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

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**Parent Equation: Domain: Range: Inverse Squared Function**

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

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**y – intercept: x – intercept: Parent Equation: Inverse Squared**

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

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**Table: x y -2 0.25 -1 1 Error 2 Parent Equation: Inverse Squared**

Function (Reciprocal of x 2) Table: x y -2 0.25 -1 1 Error 2 f(x) = 1 x 2 Parent Equation: Graph Description: Symmetrical “L” Curves in 1st and 2nd Quadrants

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Exponential Function b = base and x = exponent

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

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**y – intercept: x – intercept: Parent Equation: Exponential Function**

f(x) = 2x y – intercept: x – intercept:

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**Table: x y -2 0.25 -1 0.5 1 2 4 Parent Equation: Exponential Function**

1 2 4 Parent Equation: f(x) = 2x Graph Description: Backwards “L” Curves

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Logarithmic Function f(x) = log x

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

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**y – intercept: x – intercept: Parent Equation: Logarithmic Function**

f(x) = log x x – intercept: y – intercept:

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**Table: x y -2 Error -1 1 2 0.301 Parent Equation: Logarithmic Function**

1 2 0.301 Parent Equation: f(x) = log x Graph Description: Upside Down “L” curve in 1st and 4th Quadrant

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

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**Domain: Range: Parent Equation: Step Function (Greatest Integer)**

f(x) = [x] Domain: Range:

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**y – intercept: x – intercept: Parent Equation: Step Function**

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

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**Table: x y Parent Equation: Graph Description: Stair Steps**

Step Function (Greatest Integer) Table: x y -2 -1 1 2 Parent Equation: f(x) = [x] Graph Description: Stair Steps

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Signum Function

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Signum Function Parent Equation: Domain: Range:

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

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**Table: x y Signum Function Parent Equation:**

-2 -1 1 2 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 Parent Equation: f(x) = sin x Domain: Range:

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**y – intercept: x – intercept: Parent Equation: Sine Function**

f(x) = sin x x – intercept: y – intercept:

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**Table: x y Sine Function Parent Equation: f(x) = sin x**

-2 -1 1 0.8415 2 0.9093 Parent Equation: f(x) = sin x 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 Parent Equation: f(x) = cos x Domain: Range:

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

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**Table: x y Cosine Function Parent Equation: f(x) = cos x**

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

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Parent Functions AII.6. Functions At this point you should be very familiar with linear and absolute value functions. You should be able to ◦ Recognize.

Parent Functions AII.6. Functions At this point you should be very familiar with linear and absolute value functions. You should be able to ◦ Recognize.

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