Question

The graph of F(x), shown below, resembles the graph of G(x) = x2, but it hasbeen changed somewhat. Which of the following could be the equation of F(x)?

GOX) = x2
FOO = 5
A. F(x) = -x2 - 1
B. F(x) = 0.4x2 - 1
C. F(x) = 4x2 - 1
D. F(x) = x2 - 1

Answer 1

The graph of F(x) resembles G(x) = x^2 but has been changed. The equation that matches the given graph is F(x) = 0.4x^2 - 1.

Step-by-step explanation:

The graph of F(x) resembles the graph of G(x) = x^2 but has been changed. We need to find the equation of F(x) based on the given options. Let's analyze each option:

A. F(x) = -x^2 - 1: This equation is a reflection of the graph of G(x) about the x-axis and a downward shift by 1. It does not match the given graph.

B. F(x) = 0.4x^2 - 1: This equation scales down the graph of G(x) vertically by a factor of 0.4 and shifts it downward by 1. It matches the given graph.

C. F(x) = 4x^2 - 1: This equation scales up the graph of G(x) vertically by a factor of 4 and shifts it downward by 1. It does not match the given graph.

D. F(x) = x^2 - 1: This equation is a vertical shift of the graph of G(x) downward by 1. It matches the given graph.

Based on the analysis, the possible equation for F(x) is B. F(x) = 0.4x^2 - 1.