parent functions constant function inverse linear (identity)inverse squared absolute value...

PARENT FUNCTIONSConstant Function InverseLinear (Identity) Inverse SquaredAbsolute Value ExponentialQuadratic LogarithmicCubic SineSquare Root CosineSignum Greatest Integer

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) = awhere a = any

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Constant Function

Domain: ,

Range: 2y

Parent Equation: f(x) = 2

Constant Function

Parent Equation: f(x) = 2

x – intercept:

y – intercept: 0, 2

None

Constant Function

Graph Description: Horizontal Line

Table:x y

-2 2

-1 2

0 2

1 2

2 2Parent Equation: f(x) = 2

Linear Function(Identity)

f(x) = x

Linear Function(Identity)

Domain: ,

Range: ,

Parent Equation: f(x) = x

Linear Function(Identity)

Parent Equation: f(x) = x

x – intercept:

y – intercept: 0, 0

0, 0

Linear Function(Identity)

Parent Equation: f(x) = x

Table:x y

-2 -2

-1 -1

0 0

1 1

2 2

Graph Description: Diagonal Line

Absolute Value Function

f(x) = │x │

Absolute Value Function

Domain: ,

Range: 0,

Parent Equation: f(x) = │x │

Absolute Value Function

Parent Equation: f(x) = │x │

x – intercept:

y – intercept: 0, 0

0, 0

Absolute Value Function

Table:x y

-2 2

-1 1

0 0

1 1

2 2Parent Equation:

Graph Description: “V” - shaped

f(x) = │x │

f(x) = x 2

Quadratic Function

f(x) = x 2

Quadratic Function

Domain: ,

Range: 0,

Parent Equation:

Quadratic Function

Parent Equation:

x – intercept:

y – intercept: 0, 0

0, 0

f(x) = x 2

f(x) = x 2

Quadratic Function

Table:x y

-2 4

-1 1

0 0

1 1

2 4Parent Equation:

Graph Description: “U” - shaped

Cubic Function

f(x) = x 3

Cubic Function

f(x) = x 3

Domain: ,

Range: ,

Parent Equation:

Cubic Function

f(x) = x 3

Parent Equation:

x – intercept:

y – intercept: 0, 0

0, 0

Cubic Function

f(x) = x 3

Parent Equation:

Table:x y

-2 -8

-1 -1

0 0

1 1

2 8

Graph Description: Squiggle, Swivel

f(x) = x

Square Root Function

f(x) = x

Square Root Function

Domain: 0,

Range: 0,

Parent Equation:

f(x) = x

Square Root Function

Parent Equation:

x – intercept:

y – intercept: 0, 0

0, 0

f(x) = x

Square Root Function

Parent Equation:

Table:x y

0 0

1 1

4 2

9 3

16 4

Graph Description: Horizontal ½ of a Parabola

f(x) = 1x

Inverse Function or Rational Function(Reciprocal of x)

f(x) = 1x

Inverse Function or Rational Function(Reciprocal of x)

Parent Equation:

Domain:

, 0 0,or

Range:

, 0 0,or

f(x) = 1x

Inverse Function or Rational Function(Reciprocal of x)

Parent Equation:

x – intercept:

y – intercept: None

None

Inverse Function or Rational Function(Reciprocal of x)

Table:x y

-2 -0.5

-1 -1

0 Error

1 1

2 0.5f(x) = 1x

Parent Equation:

Graph Description: Opposite “L” Curves in 1st and 3rd

Quadrants

Inverse Squared Function

(Reciprocal of x 2)

f(x) = 1x 2

Inverse Squared Function

(Reciprocal of x 2)

f(x) = 1x 2Parent Equation:

Domain:

, 0 0,or

Range:

0,

Inverse Squared Function

(Reciprocal of x 2)

f(x) = 1x 2

x – intercept:

y – intercept: None

None

Parent Equation:

Inverse Squared Function

(Reciprocal of x 2)

f(x) = 1x 2Parent Equation:

Table:x y

-2 0.25

-1 1

0 Error

1 1

2 0.25

Graph Description: Symmetrical “L” Curves in 1st and 2nd

Quadrants

Exponential Function

( ) xf x b

b = base and

x = exponent

f(x) = 2x

Exponential Function

Domain: ,

Range: 0,

Parent Equation:

f(x) = 2x

Exponential Function

x – intercept:

y – intercept: 0, 1

None

Parent Equation:

f(x) = 2x

Exponential Function

Table:x y

-2 0.25

-1 0.5

0 1

1 2

2 4Parent Equation:

Graph Description: Backwards “L” Curves

f(x) = log x

Logarithmic Function

f(x) = log x

Logarithmic Function

0,

Range: ,

Parent Equation:

Domain:

f(x) = log x

Logarithmic Function

x – intercept:

y – intercept: None

1, 0

Parent Equation:

Logarithmic Function

Table:x y

-2 Error

-1 Error

0 Error

1 0

2 0.301

Parent Equation: Graph Description: Upside Down “L” curve in

1st and 4th Quadrant

f(x) = log x

Step Function(Greatest Integer)

f(x) = [x]

Step Function(Greatest Integer)

f(x) = [x]

Domain: ,

Range: y y Z

Parent Equation:

Step Function(Greatest Integer)

f(x) = [x] Parent Equation:

x – intercept:

y – intercept: 0, 0

0, 1

Step Function(Greatest Integer)

f(x) = [x] Parent Equation:

Graph Description: Stair Steps

Table:x y-2 -2

-1 -1

0 0

1 1

2 2

Signum Function

Signum Function

Domain: ,

Range: 1, 0, 1y

Parent Equation:

Signum Function

Parent Equation:

x – intercept:

y – intercept: 0, 0

0, 0

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 Functionf(x) = sin x

Sine Function

f(x) = sin x

Domain: ,

Range: 1, 1

Parent Equation:

Sine Function

f(x) = sin x

x – intercept:

y – intercept: 0, 0

,x x n n Z

Parent Equation:

Sine Function

f(x) = sin x

Table:x y-2 -0.9093

-1 -0.8415

0 0

1 0.8415

2 0.9093

Parent Equation: Graph Description: Wavy, above and below x-axis

with y-int at (0, 0)

Cosine Functionf(x) = cos x

Cosine Function

f(x) = cos x

Domain: ,

Range: 1, 1

Parent Equation:

Cosine Functionf(x) = cos x

x – intercept:

y – intercept: 0, 1

,2

x x n n Z

Cosine Function

f(x) = cos x

Table:

x y-2 -0.4161

-1 0.5403

0 1

1 0.5403

2 -0.4161

Parent Equation: Graph Description: Wavy, above and below x-axis

with y-int at (0, 1)