The tables show values of the cubic function g(x)

Question

after a transformation of the cubic function f(x)
.

x
f(x)

−2
−6

−1
1

0
2

1
3

2
10

x
g(x)

−2
6

−1
−1

0
−2

1
−3

2
−10

What transformation was applied to f(x)
to obtain g(x)
?(1 point)
Responses

Reflection across the y-axis
Reflection across the y -axis

Reflection across the x-axis
Reflection across the x -axis

Horizontal dilation by a scale factor of 2
Horizontal dilation by a scale factor of 2

Vertical dilation by a scale factor of 2
Vertical dilation by a scale factor of 2

Answer 1

To determine the transformation applied to the function \( f(x) \) to obtain \( g(x) \), we can compare the values of \( f(x) \) and \( g(x) \):

• For \( x = -2 \):

  • \( f(-2) = -6 \)
  • \( g(-2) = 6 \)

• For \( x = -1 \):

  • \( f(-1) = 1 \)
  • \( g(-1) = -1 \)

• For \( x = 0 \):

  • \( f(0) = 2 \)
  • \( g(0) = -2 \)

• For \( x = 1 \):

  • \( f(1) = 3 \)
  • \( g(1) = -3 \)

• For \( x = 2 \):

  • \( f(2) = 10 \)
  • \( g(2) = -10 \)

From this comparison, we see that the values of \( g(x) \) are the negative of the corresponding values of \( f(x) \).

This indicates that the transformation applied is a reflection across the x-axis, which changes the sign of all output values.

Answer: Reflection across the x-axis