Question

Let g(x) vertical shift of f(x)=-x up 3 units followed by a vertical stretch by a factor of 4. Write the rule for g(x).

Answer 1

Given:

g(x) vertical shift of $f(x)=-x$ up 3 units followed by a vertical stretch by a factor of 4.

To find:

The rule for g(x).

Solution:

We have,

$f(x)=-x$

This function shifts 3 units up. So,

$f(x)+3=-x+3$

This function vertical stretch by a factor of 4. So,

$g(x)=4(f(x)+3)$

$g(x)=4(-x+3)$

$g(x)=-4x+12$

Therefore, the rule for g(x) is $g(x)=-4x+12$.