Question

Let g(x) be the reflection of f(x) = x 2 + 3 in the x-axis. What is the function rule for g(x)?

Answer 1

g(x) will be g(x)=-2x-3 because it is a reflection of f(x) over the x-axis. F(x)'s reflection over the x-axis will become -f(x).

Answer 2

`g(x)=-x^2-3`

Explanation:

The parent function is
`x^2+3`

Now, the function g(x) is obtained by reflecting the graph of f(x) about the x-axis.

When the parent function f(x) is reflected about the x-axis then the translated function is -f(x)

Therefore, we have g(x)=-f(x)

Hence, the equation of g(x) is

`g(x)=-f(x)\\\\g(x)=-(x^2+3)\\\\g(x)=-x^2-3`