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

Question

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

x
f(x)
−1
2
0
−1
1
−2
2
−1
3
2
x
g(x)
−12
2
0
−1
12
−2
1
−1
32
2
What transformation was applied to f(x)
to obtain g(x)
?(1 point)
Responses

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

Reflection across the y
-axis
Reflection across the y -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

Answer 1

To determine the transformation applied to \( f(x) \) to obtain \( g(x) \), we can analyze the values of the two functions.

Let's compare the y-values of \( f(x) \) and \( g(x) \) at corresponding x-values.

1. For \( x = -1 \):

   • \( f(-1) = 2 \)
   • \( g(-12) = 2 \)

2. For \( x = 0 \):

   • \( f(0) = -1 \)
   • \( g(0) = -1 \)

3. For \( x = 1 \):

   • \( f(1) = -2 \)
   • \( g(12) = -2 \)

4. For \( x = 2 \):

   • \( f(2) = -1 \)
   • \( g(1) = -1 \)

5. For \( x = 3 \):

   • \( f(3) = 2 \)
   • \( g(32) = 2 \)

From the above comparison, we notice that the y-values of \( g(x) \) appear to correspond to the y-values of \( f(x) \) with their signs changed.

Thus, it appears that each \( g(x) \) value is \( -f(x) \). This indicates that there is a reflection across the x-axis.

Therefore, the correct transformation from \( f(x) \) to \( g(x) \) is:

Reflection across the x-axis.