Question

The functions f(x) and g(x) are shown on the graph.
f(x) = x2
What is g(x)?
10-
If(x)
1
х
10
-5
5
10
g(x)
-10
A. g(x) = (– x)2 - 3
B. g(x) = – x2 + 3
c. g(x) = (-x)2 + 3
D. g(x) = -X2 - 3

Answer 1

Answer:

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

Step-by-step explanation:

Given

$f(x) = x^2$

Required

Determine g(x)

First, shift f(x) down by 3 units

The rule is:

$f'(x) = f(x) - 3$

So:

$f'(x) = x^2 - 3$

Next, reflect f'(x) across the x-axis to get g(x)

The rule is:

$g(x) = -f(x)$

So, we have:

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

Open bracket

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