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# PARENT FUNCTIONS Constant Function Inverse

## Presentation on theme: "PARENT FUNCTIONS Constant Function Inverse"— Presentation transcript:

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 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

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

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

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

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

Linear Function (Identity) f(x) = x

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

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

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

Absolute Value Function f(x) = │x │

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

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

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

Quadratic Function f(x) = x 2

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

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

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

Cubic Function f(x) = x 3

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

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

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

Square Root Function f(x) = x

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

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

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

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

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

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

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

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

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

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

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

Exponential Function b = base and x = exponent

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

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

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

Logarithmic Function f(x) = log x

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

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

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

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

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

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

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

Signum Function

Signum Function Parent Equation: Domain: Range:

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

Table: x y Signum Function Parent Equation:
-2 -1 1 2 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:

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

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)

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:

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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