Question

USE STRUCTURE Complete the table to show the effect that the transformation has on the table of the parent function f(x)=x2

.

g(x)
is a reflection of f(x)
across the x-axis.

x f(x) g(x)
-2 4
-1 1
0 0
1 1
2 4

Answer 1

x f(x) g(x)

-2 4 -4

-1 1 - 1

0 0 0

1 1 -1

2 4 -4

Explanation:

When a point is reflected across the x-axis the reflected point will have the same x value as the pre-image point

Therefore if point(x, y) is reflected across the x-axis the reflected point will be (x, -y)

When f(x) = x² is reflected across the x-axis, the reflected function becomes

f'(x) = -f(x) = -x²

Using this information we can complete the table as follows:

x f(x) g(x)

-2 4 -4

-1 1 - 1

0 0 0

1 1 -1

2 4 -4