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?
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
But if I plot f(x) = -3x + 5 and -f(x) = 3x - 5, it does not give me the reflection.
do the graphs at wolframalpha.com match your own? There, the two lines are clearly reflections in the x-axis.
When reflecting a function over the x-axis, you need to change the sign of the function. So, if the original function is f(x) = -3x + 5, reflecting it over the x-axis would be -f(x) = -(-3x + 5). Simplifying this gives you f(x) = 3x - 5.
To explain how this transformation is done:
1. Start with the original function f(x) = -3x + 5.
2. To reflect over the x-axis, we change the sign of the function. So, we replace f(x) with -f(x).
3. Therefore, the new equation after reflecting over the x-axis is -f(x) = -(-3x + 5).
4. Simplifying the equation gives us f(x) = 3x - 5.
So, the correct equation for reflecting f(x) = -3x + 5 over the x-axis is f(x) = 3x - 5.