Question

The function f(x) = -5x. The graph of g(x) is f(x) vertically compressed by a factor of 1/4 and reflected in the x axis. What is the function rule for g(x)?

g(x) = -20x
g(x) = -5/4x
g(x) = 20x
g(x) = -3x + 2

Answer 1

None of the above are correct, the correct answer is 
g(x)=5/4x
because you multiply by 1/4 (the vertical, or towards the x axis compression) to get -5/4x 
but then you have to reflect across the x axis by flipping the sign to get 5/4x
Try using a graphing tool to experiment with how changing numbers affects the line. 

Answer 2

Answer:  $g(x)=\dfrac{5}{4}x$

Step-by-step explanation:

We know that when we compress function h(x) by scale factor 'a', then the new compress function is represented as :-

$H(x)=a (\text{h(x)})$

Given : The function $f(x) = -5x$

The graph of g(x) is f(x) vertically compressed by a factor of$\dfrac{1}{4}$and reflected in the x axis.

Then , the function rule for F(x) after vertically compressed by a factor of$\dfrac{1}{4}$ will be :-

$F(x)=\dfrac{1}{4}f(x)=\dfrac{1}{4}(-5x)\\\\\Rightarrow\ F(x)=\dfrac{-5}{4}x$

After reflection across x-axis (sign gets change) the new function becomes :_

$g(x)=-F(x)=\dfrac{5}{4}x$