Question

Given f(x)=|x+2|, write a function g(x) such that the line moves left 2 units and compresses by 1/3. HELP PLEASE!

Answer 1

To make it "move left" 2, think about the value of f(x) when x = -2 .... it's f(x) = 0.

For x values less than -2, the absolute value returns a positive f(x), and for x values greater than -2, it also returns values for f(x) that are positive. So it's a V-shaped graph that touches the x-axis at x = -2.

To move it left by two positions to make g(x), you need a similar V-shape to touch the x axis at x = -4... so if you didn't have to worry about the compressing, it would be like |x+4|.

The "compress by 1/3" is confusing... It probably means make it 1/3 as wide a V-shape. This means you need a coefficient to change the slope of the two sides of the V... right now, they have slope of 1 (on the right side of the V) and -1 (on the left side of the V).

Answer 2

Ok, i kinda get the jist of it. In the textbook, it didnt give the problem like this so i dont know how to solve it; my teacher just did it backwards i guess. Thank you though! it's starting to make sense the more i do it. :)

Answer 3

the main thing that really gets to me is the compressions. i will ask my teacher some more about it