Function Family Album

Exponential

Real World Example

Transformations

Y=a(x-h)^2+k

a = vertical stretch/compression, h = horizontal shift, k = vertical shift

Vertical Stretch

Horizontal Shift

Vertical Shift

Parent Function

Y=10^x

x-int=N/A y-int=1

Y=2(x)^2

Y=(x-1)^2

Y=(x)^2+1

Transformations

Domain

(-∞,∞)

Range

[0,∞)

Domain

(-∞,∞)

Range

[1,∞)

Domain

(-∞,∞)

Range

(0,∞)

Y=a^(x-h)+k

X

-2

-1

0

1

Y

0.01

0.1

1

10

a = vertical stretch/compression, h = horizontal shift, k = vertical shift

Real World Example

Vertical Shift

Horizontal Shift

Vertical Stretch

Quadratic

Y=10^x -1

Y=10^(x-1)

Y=15^x

Inverse

y=log x

Parent Function

Y=X^2

x-int=0 y-int=0

Y-Axis

Domain

(-∞,∞)

Range

(0,∞)

Domain

(-∞,∞)

Range

(-1,∞)

Domain

(-∞,∞)

Range

(0,∞)

Asymptope: y=0

Domain

(-∞,∞)

Range

[0,∞)

X-Axis

X

-1

0

1

2

Y

1

0

1

4

Y-Axis

X-Axis

Inverse

Y^2=X

Linear

Parent Function

Y=X

x-int=0 y-int=0

Slope (m)

Domain

(-∞,∞)

Range

(-∞,∞)

Piecewise

X

-1

0

1

2

Y

-1

0

1

2

Y-int (b)

Y-Axis

Y=|x|+1

Equation

x+3 x<-3

Y= x^2 -3≤x≤3

|x-5|-1 x>3

Domain

(-∞,∞)

Range

[1,∞)

{

Domain

(-∞,∞)

Range

[-∞,∞)

Real life Example

X-Axis

Transformations

Y=(ax-h)+k

X

-5

-3

3

5

Y

-2

9

9

-1

a = vertical stretch/compression, h = horizontal shift, k = vertical shift

Y-Axis

Vertical Shift

Horizontal Shift

Vertical Stretch

Y=(x-2)

Y=(x)+2

Y=(2x)

Function Family Album Project

Domain

(-∞,∞)

Range

(-∞,∞)

X-Axis

Real World Example

Transformations

Y=a√(x-h)+k

a = vertical stretch/compression, h = horizontal shift, k = vertical shift

Vertical Shift

Vertical Stretch

By: Dax Robinson

Horizontal Shift

Y=2√(x)

Y=√(x)+1

Parent Function

Y=√x

x-int=0 y-int=0

Domain

[0,∞)

Range

[0,∞)

Domain

[0,∞)

Range

[1,∞)

Y=√(x-1)

Square Root

Domain

[1,∞)

Range

[0,∞)

Domain

[0,∞)

Range

[0,∞)

X

0

1

4

9

Y

0

1

2

3

Y-Axis

Absolute Value

Real World Example

X-Axis

Parent Function

Y=|x|

x-int=0 y-int=0

Inverse

√y=x

X

-1

0

1

2

Domain

(-∞,∞)

Range

[0,∞)

Y

1

0

1

2

Transformations

Logarithmic

Y=a log (x-h)+k

Transformations

a = vertical stretch/compression, h = horizontal shift, k = vertical shift

Horizontal Shift

Vertical Shift

Vertical Stretch

Y=a|x-h|+k

a = vertical stretch/compression, h = horizontal shift, k = vertical shift

Real World Example

Vertical Shift

Horizontal Shift

Vertical Stretch

Parent Function

Y= log x

x-int=0 y-int=0

Y-Axis

Y= log (x) +1

Y= 2 log (x)

Y= log (x-1)

Inverse

|y|=x

Y=|x-1|

Y=|x|+1

Y=2|x|

Domain

(0,∞)

Range

(-∞,∞)

Domain

(1,∞)

Range

(-∞,∞)

Domain

(0,∞)

Range

(-∞,∞)

Domain

(-∞,∞)

Range

[1,∞)

Domain

(-∞,∞)

Range

[0,∞)

Domain

(0,∞)

Range

(-∞,∞)

X-Axis

X

0.01

0.1

1

10

Y

-10

-1

0

1

Inverse

y=10^x

Y-Axis

X-Axis