Question

What transformations to the linear parent function, f(x) = x, give the function

g(x) = 4x - 2? Select all that apply.
A. Shift down 2 units.
B. Vertically stretch by a factor of 4.
O c. Horizontally stretch by a factor of 4.
O D. Shift left 2 units.​

Answer 1

A. Shift down 2 units.

B. Vertically stretch by a factor of 4.

Explanation:

Given the function

f(x)=x

If we stretch y vertically by a factor of m, we have: y=m·f (x)

Therefore:

Vertically stretching f(x) by a factor of 4, we have: 4x.

Next, if we take down f(x) by k units we have: y= f(x)-k

Therefore: Taking down 4x by 2 units, we obtain:

g(x)=4x-2

Therefore, Options A and B applies.