Question

Describe using words in a sentence the transformations that must be applied to the graph of f to obtain thegraph of g(x) = -2 f(x) + 5.

Answer 1

we have

f(x)

and

g(x)=-2f(x)+5

so

step 1

First transformation

Reflection about the x-axis

so

f(x) -----> -f(x)

step 2

Second transformation

A vertical dilation with a scale factor of 2

so

-f(x) ------> -2f(x)

step 3

Third transformation

A translation of 5 units up

so

-2f(x) -------> -2f(x)+5