Question

Which of the following describes the transformations of g(x)=-(2)x+4-2 from the parent function f(x)=2x

Answer 1

This graph has a few changes. It is reflected across the axis, then shifted left 4 units. it is also shifted down two units. 

Answer 2

function f(x) first reflect across x axis and then shifted 4 unit up and then 2 unit down.

Explanation:

Given : Transformations of g(x)=-(2)x+4-2 from the parent function f(x)=2x.

To find : Which of the following describes the transformations.

Solution : We have given

Parent function f(x) = 2x.

Transformed function g(x) = -(2)x+4-2.

By the transformation rule : (1) reflection across x - axis f(x) →→ -f(x) .

(2) f(x) →→ f(x) + k it mean function shifted up by k unit.

(3) f(x) →→ f(x) - k it mean function shifted down by k unit.

Then

f(x) = 2x →→→→-(2)x+4-2.

It mean function f(x) first reflect across x axis and then shifted 4 unit up and then 2 unit down.

Therefore, function f(x) first reflect across x axis and then shifted 4 unit up and then 2 unit down.