Question

Describe the transformations from the parent function f(x)=x^2 to the function g(x+2)^2+5

Answer 1

Answer:

The parent function is the simplest form of the type of function given.

g

(

x

)

=

x

2

The transformation being described is from  

g

(

x

)

=

x

2

to  

f

(

x

)

=

x

2

.

g

(

x

)

=

x

2

→

f

(

x

)

=

x

2

The horizontal shift depends on the value of  

h

. The horizontal shift is described as:

f

(

x

)

=

f

(

x

+

h

)

- The graph is shifted to the left  

h

units.

f

(

x

)

=

f

(

x

−

h

)

- The graph is shifted to the right  

h

units.

In this case,  

h

=

0

which means that the graph is not shifted to the left or right.

Horizontal Shift: None

The vertical shift depends on the value of  

k

. The vertical shift is described as:

f

(

x

)

=

f

(

x

)

+

k

- The graph is shifted up  

k

units.

f

(

x

)

=

f

(

x

)

−

k

- The graph is shifted down  

k

units.

In this case,  

k

=

0

which means that the graph is not shifted up or down.

Vertical Shift: None

The graph is reflected about the x-axis when  

f  (

x

)

=

−

f

(

x

)

.

Reflection about the x-axis: None

The graph is reflected about the y-axis when  

f

(

x

)

=

f

(

−

x

)

.

Reflection about the y-axis: None

Compressing and stretching depends on the value of  

a

.

When  

a

is greater than  

1

: Vertically stretched

When  

a

is between  

0

and  

1

: Vertically compressed

Vertical Compression or Stretch: None

Compare and list the transformations.

Parent Function:  

g

(

x

)

=

x

2

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

image of graph