quadric and parabola

Question

The range of f(x) = ax+b is the set of all real numbers. Which produces a counter example to her statement?

 

A. b=0

B. a<0

C. a=0

D. b<0

Answer 1

(C) a = 0 produces a counter example.

If a = 0, then we have

f(x) = 0x + b

or

f(x) = b , which is a horizontal line.

Thus, the range (all possible values of "y") is limited to whatever "b" is.