Question

For f(x) = 2|x+3| – 5, name the type of function and describe each of the three transformations from the parent function f(x) = |x|.

Answer 1

Type of function: Absolute Value

Transformations: 1) elongated by a stretch factor of 2; 2) shifted left 3; 3) shifted down 5

Answer 2

Shifted 5 units down

Shifted 3 units to the left

Vertically streched by a scale of 2.

Explanation:

The parent function is

`f(x)=|x|`

The transformed function is

`g(x)=2|x+3|-5`

You can deduct by comparison, that the function was shifted 5 units down, 3 units to the left, and vertically streched by a scale of 2.

We deduct this transfromations based on the following rules.

`f(x)-u` indicates a movement downside
`u` units.

`f(x+u)` indicates a movement leftside
`u` units.

`uf(x)` indicates a vertical stretch for
`u>1`.