Question

The graph of F(x), shown below, resembles the graph of G(x) = x, but it has

been changed somewhat. Which of the following could be the equation of
F(x)?
5
GX = x2
6
A. F(x) = -(x - 2)2 - 1
B. F(x) = (x - 2)2 - 1
C. F(x) = (x + 2)2 - 1
D. F(x) = -(x + 2)2 - 1​

Answer 1

Option (A)

Explanation:

Parent function is given as G(x) = x²

If this function is reflected over the x-axis then the new function will be,

G'(x) = -x²

Then shifted 2 units right,

G"(x) = -(x - 2)²

Followed by the shifting of 1 unit down,

F(x) = -(x - 2)² - 1

Therefore, translated function of the given parent function will be,

F(x) = -(x - 2)² - 1

Option (A) is the answer.