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

Answer:

Type of function: Absolute Value

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

Answer 2

Answer:

Shifted 5 units down

Shifted 3 units to the left

Vertically streched by a scale of 2.

Step-by-step 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 $u>1$.