Question

Let g(x) be the reflection of f(x) = x2 +3 in the x-axis. What is the function rule for g(x)? A. g(x) = -x2 - 3 B. g(x) = -x2 + 3 C. g(x) = x2 - 3 D. g(x) = x2 + 3

Answer 1

if it is its reflection it means it its opposite. To determine an opposite, you can put - in front of the ecuation ( or number). So -( x2+3)=-x2-3
the correct answer is A

Answer 2

Option A is correct.

Function rule for g(x) is;

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

Explanation:

Given the statement:
`f(x)=y = x^2+3`

To find the function rule for g(x).

The rule of reflection across x-axis is given by;

`(x, y) \rightarrow (x, -y)`

Apply this rule on f(x) we have;

`-y = x^2+3`

`y =-(x^2+3)`

or

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

Therefore, the function rule for g(x) is,
`g(x) = -x^2-3`