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 correct answer. The answer options are..

Horizontal stretch

vertical stretch

horizontal shrink

vertical shrink

its asking which one of these transformations/dilations makes the first equation into the second one? Please help me!

Answer 1

the plus 9 is shifting your function up by 9 units on the y axis. So a similar, easier question would be for |x| and 4|x|. The answers to these questions will be the same.

The multiplication by 4 takes some point (x,y) on the old graph to (x,4*y) on the new graph. So for the same horizontal position, the vertical position is made larger for positive values and smaller for negative values (if there were any).

So, this is a vertical stretch.