If I want to reflect f(x) = -3x + 5 over the x-axis, would the new equation be f(x) = 3x - 5? Or is it -f(-x) = 3x - 5?

Answer 1

to reflect over the x-axis, y values change sign. So,

f(x) -> -f(x), so it is -f(x) = 3x-5

Note that -f(-x) = -(-3(-x)+5) = -(3x+5) = -3x-5

See the reflection at

http://www.wolframalpha.com/input/?i=plot+y%3D-3x%2B5%2C+y%3D3x-5

Answer 2

But if I plot f(x) = -3x + 5 and -f(x) = 3x - 5, it does not give me the reflection.

Answer 3

do the graphs at wolframalpha.com match your own? There, the two lines are clearly reflections in the x-axis.