Question

State the order and type of each transformation of the graph of the function ƒ(x) = –|(x + 6)| + 4 as compared to the graph of the base function.

A) left 6 units, up 4 units, reflection about the x-axis

B) left 6 units, reflection about the x-axis, up 4 units

C) right 6 units, up 4 units, reflection about the y-axis

D) left 6 units, reflection about the y-axis, up 4 units

Answer 1

A) left 6 units, up 4 units, reflection about the x-axis

Explanation:

`f(x) = -|x + 6| + 4`

For absolute function , the parent function is
`f(x)=|x|`

f(x) ---> f(x+a) , the graph will be shifted 'a' units to the left

6 is added with x so, we move graph 6 units left.

f(x) ---> f(x)+a , the graph will be shifted 'a' units up

4 is added with x. So, we move graph 4 units up

f(x) ---> -f(x) , the graph will be reflected over x-axis

we have negative sign in the front of the equation, so there will be a reflection about the x-axis

The order of transformation is

moving left 6 units, moving up by 4 units and a reflection about x-axis

Answer 2

A) left 6 units, up 4 units, reflection about the x-axis

Explanation:

The given absolute value function is

ƒ(x) = –|(x + 6)| + 4

The base function is

`g(x)=|x|`

There is a transformation of the form;

`-g(x+b)+c`

The base function is shifted left 6 units. (+b means left shift) and shifted up 4 units (+4 means upward vertical shift), and reflected in the x-axis , (-g(x)) means reflection in the x-axis.

The correct choice is A.