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

Answer:

Option A is correct.

Function rule for g(x) is;

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

Step-by-step 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, $g(x) = -x^2-3$

Answer 2

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