Question

I know the answer is A, but I'm not sure how they got it.

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Answer 1

Plot the graph separately for different parts of the domain.

Answer 2

For x<0 plot y=4x and for x>=0 plot y=-4x and you'll get option A.

Answer 3

for x<0 means for all x's on the left side of the y-axis.
y= 4x or (so we can
match that up with y = m x + b
y = 4 x + 0
that is a line with slope +4 and y-intercept of 0

if you plotted y= 4x (and ignored the x values) it would go through 0,0 and 1,4
and it would look like this

Answer 4

but if we stop it once we reach x=0, we are left with this

Answer 5

now plot y = -4x
it has a slope of -4 and goes through (0,0)
it looks like this

Answer 6

if we only plot that for x>=0 we get just the right side.
putting the two plots together, we get the answer.

Of course, you have to know how to plot lines to do this.
If that is where you are stuck you can review at
https://www.khanacademy.org/math/algebra-basics/core-algebra-graphing-lines-slope/core-algebra-graphing-slope-intercept/v/graphing-a-line-in-slope-intercept-form

Answer 7

If this is not clear, please post a follow-up question.