PARENT FUNCTIONS Constant Function Inverse Linear Identity Inverse

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

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

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

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

Constant Function Table: Parent Equation: f(x) = 2 x -2 -1 0 1 2 Graph Description: Horizontal Line y 2 2 2

Linear Function (Identity) f(x) = x

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

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

Linear Function (Identity) Table: Parent Equation: f(x) = x x -2 -1 0 1 2 Graph Description: Diagonal Line y -2 -1 0 1 2

Absolute Value Function f(x) = │x │

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

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

Absolute Value Function Table: Parent Equation: f(x) = │x │ x -2 -1 0 1 2 Graph Description: “V” - shaped y 2 1 0 1 2

Quadratic Function f(x) = x 2

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

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

Quadratic Function Table: x -2 -1 0 1 2 Parent Equation: f(x) = x 2 Graph Description: “U” - shaped y 4 1 0 1 4

Cubic Function f(x) = x 3

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

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

Cubic Function Table: x -2 -1 0 1 2 y -8 -1 0 1 8 Parent Equation: f(x) = x 3 Graph Description: Squiggle, Swivel

Square Root Function f(x) = x

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

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

Square Root Function Table: Parent Equation: f(x) = x x 0 1 4 9 16 y 0 1 2 3 4 Graph Description: Horizontal ½ of a Parabola

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

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

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

Inverse Function or Rational Function (Reciprocal of x) Table: x -2 -1 0 1 2 1 Parent Equation: f(x) = x Graph Description: Opposite “L” Curves in 1 st and 3 rd y -0. 5 -1 Error 1 0. 5

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

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

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

Inverse Squared Function (Reciprocal of x 2) Table: 1 Parent Equation: f(x) = 2 x x -2 -1 0 1 2 y 0. 25 1 Error 1 0. 25 Graph Description: Symmetrical “L” Curves in 1 st and 2 nd

Exponential Function b = base and x = exponent

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

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

Exponential Function Table: x -2 -1 0 1 2 Parent Equation: f(x) = 2 x Graph Description: Backwards “L” Curves y 0. 25 0. 5 1 2 4

Logarithmic Function f(x) = log x

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

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

Logarithmic Function Table: x -2 -1 0 1 2 y Error 0 0. 301 Parent Equation: f(x) = log x Graph Description: Upside Down “L” curve in 1 st and 4 th Quadrant

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

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

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

Step Function (Greatest Integer) Table: x y -2 -2 -1 -1 0 0 1 1 2 2 Parent Equation: f(x) = [x] Graph Description: Stair Steps

Signum Function

Signum Function Parent Equation: Domain: Range:

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

Signum Function Table: x y -2 -1 -1 -1 0 0 1 1 2 1 Parent Equation: Graph Description: Left and Right Arrows Opposite Directions

Sine Function f(x) = sin x

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

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

Sine Function Table: x y -2 -0. 9093 -1 -0. 8415 0 0 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)

Cosine Function f(x) = cos x

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

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

Cosine Function Table: Parent Equation: x y -2 -0. 4161 -1 0. 5403 0 1 1 0. 5403 2 -0. 4161 f(x) = cos x Graph Description: Wavy, above and below x-axis with y-int at (0, 1)