Question

Write a function g whose graph represents a reflection in the x-axis of the graph of f(x)=1/2x-3

Answer 1

Answer: g(x) = -(1/2)*x + 3.

Explanation:

First, let's define a reflection over the x-axis.

If we have a point (x, y) and we reflect it over the x-axis, our new point will be (x, -y).

Now, when we have a function

f(x) = y, the points can be written as:

(x, y = f(x) ) = (x, f(x))

Then, after the reflection over the x-axis, we have:

(x, y = g(x)) = (x, -f(x))

So now we have g(x) = -f(x)

and we know that f(x) = (1/2)*x - 3

then our new function is g(x) = y = -f(x) = -( (1/2)*x - 3) = -(1/2)*x + 3.

g(x) = -(1/2)*x + 3.