What are 2 similarities that identity function and absolute function have?

Question

This is just a simple question that I can't figure out. Help me please!

Answer 1

Hi Yenna,

 

I'll denote the two functions as f_i for identity, and f_a for absolute value. The identity function is f_i(x) = x. The absolute value function is f_a(x) = |x|.

 

1) For x<0, f_i(x) = x; for example f_i(-2) = -2. However, f_a(x) = -x; for example f_a(-2) = |-2| = 2. We see that f_i has a slope of +1, and f_a has a slope of -1. Therefore, the similarity is that the magnitude (that is, absolute value) of the slopes is the same.

 

2) For x ≥ 0, ...

 

Yenna, I'll let you finish the second similarity. Good luck !