Question

F(x) = { x + 7 and g(x) = -x + 7 What transformation occurs from function f to function g?

Answer 1

Answer:  Reflect over the y axis

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Explanation:

We have these two given functions

• f(x) = x+7
• g(x) = -x+7

The change is that the x has been replaced with -x

We can say

f(x) = x+7

f(-x) = -x+7 ... replace each x with -x

g(x) = f(-x)

g(x) = -x+7

When we replace x with -x, we're flipping the x inputs from positive to negative, and vice versa. This visually will reflect the line over the vertical y axis. A point like (1,8) on f(x) reflects over to (-1,8) on g(x).

As another example, the point (-5,2) on f(x) reflects over the y axis to arrive at (5,2) on the g(x) function.