If f(x) = the absolute of x + 5, then the graph of f shifted 5 units down can be represented by what equation?

Question

A) F(x) = absolute value of x

B) F(x) = absolute value of x -5

C) F(x) = 5 times absolute value of x -5

D) F(x) = absolute value of x and -5

E) None of the above

Super confused! Please answer!

Answer 1

The answer is actually E !!

Reason for it is it tells you the function shifts 5 down meaning the y values change by moving 5 in negative direction! It is not moving in the x direction. The x direction movement is what is "strapped to x in the absolute value part of the function . Here it is the (x+5) in the absolute value sign meaning it moves minus 5 from (0,0) in the x direction (which is the opposite of the +5 part of the term.

The actual function shift would be f(x_shift)= (absolute value(x+5)) - 5