Question

Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function.

h(x) = 2 | x | + 2

Answer 1

Multiplying the |x| by 2 stretches the graph vertically by a factor 2.
Then a translation of the graph 2 upwards parallel to y axis gives us
h(x) = 2 |x| + 2.

Answer 2

The parent function f(x) is given by:

`f(x)=|x|`

The transformed function h(x) is given by:

`h(x)=2|x|+2`

We know that the graph of the function g(x) is a vertical stretch of the graph of the parent function plus a translation of the function 2 units up.

( Since if f(x) → a f(x)

Then the function is a vertical stretch if |a|>1 and a vertical compression if 0<|a|<1

Also, a function f(x) → f(x)+k is shifted k units up or down depending on whether k>0 or k<0 respectively )