Question

If the graph of y=f(x),xER is the same as y= |f(x)|,xER then...

A. f(x) may be of the form ax + b ,a (cant equal) 0 or of the form ax^2+bx+c, a (cant equal) 0
B. f(x) may be of the form ax + b,a c (cant equal) 0 but cannot be of the form ax^2+bx+c, a (cant equal) 0
C. f(x) may be of the form ax^2+bx+c, a (cant equal) 0 , but cannot be of the form ax + b,a c (cant equal) 0
D. f(x) cannot be of the form ax^2+bx+c, a (cant equal) 0 or ax + b,a c (cant equal) 0

*I put cant equal in place of the equal signs that have slashes on them

Answer 1

recall the definition of |x|
|x| = x if x >= 0
|x| = -x if x < 0
so, you know that f(x) is never negative
a sloping straight line cannot satisfy that condition, but a quadratic (such as f(x) = x^2) can.