What kind of transformation converts the graph of f(x)=|x|+9 into the graph of g(x)=4|x|+9?

Question

There is only one right answer.

Here are the options...

Vertical stretch

vertical shrink

horizontal stretch

horizontal shrink

Answer 1

When you have a function g(x) = af(x) and "a" is > 1, you will have a vertical stretch. You are stretching the graph away from the x-axis. If 0 < a < 1, you have a vertical compression (shrink). This is when you are compressing the graph towards the x-axis.

In your example both f(x) and g(x) have a vertical shift up of 9 units.

g(x) = 4|x| + 9 adds the vertical stretch.

Answer: g(x) has an additional vertical stretch

Answer 2

the graph is a V shape, opening upward, of two lines intersecting at (0,9)

by changing the coefficient to 9, the V shape becomes more narrow, more vertical.

It increases vertically faster, by 9 fold.

Like parabolas that open upward in a somewhat similar manner, the transformation

involves vertical stretching.

(I'd add that it's similar to horizontal shrinking, except that likely is reserved for the V shapes that open horizontally, left and right, not up or down.