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A parabola is drawn on a coordinate plane. Both axes range from negative 5 to 5 in one-unit increments.

The original graph of the function y=f(x)
is shown. Select the table that represents y=f(−x)
.

(1 point)
Responses

x f(−x)
−1
−2
−2
0
−3
−2
x f left parenthesis negative x right parenthesis negative 1 negative 2 negative 2 0 negative 3 negative 2

x f(−x)
1 −2
2 0
3 −2
x f left parenthesis negative x right parenthesis 1 negative 2 2 0 3 negative 2

x f(−x)
−1
2
−2
0
−3
2 x f left parenthesis negative x right parenthesis negative 1 2 negative 2 0 negative 3 2

x f(−x)
1 2
2 0
3 2

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

To determine the table that represents ( y = f(-x) ) based on the original graph of ( y = f(x) ), we need to identify the points of the original parabola and find their corresponding values when ( x ) is replaced by ( -x ).

Since the original function is mirrored about the y-axis when we evaluate ( f(-x) ), we need to switch the signs of the x-values in each ordered pair, while retaining the y-values.

If we denote original points as ( (x, f(x)) ), the new points for ( f(-x) ) will be ( (-x, f(x)) ).

Assuming the original graph provided points similar to:

  • ( (1, -2) )
  • ( (2, 0) )
  • ( (3, -2) )

Then the corresponding points for ( f(-x) ) would become:

  • ( (-1, -2) )
  • ( (-2, 0) )
  • ( (-3, -2) )

So from the given responses, we need to find the one that shows:

  • When ( x = -1 ), ( f(-x) = -2 )
  • When ( x = -2 ), ( f(-x) = 0 )
  • When ( x = -3 ), ( f(-x) = -2 )

Thus the correct table option is:

( x, f(-x) )

  • (-1, -2)
  • (-2, 0)
  • (-3, -2)

This is the representation of ( y = f(-x) ) based on the reflection of the original function.

From the provided options, look for the one that matches ( (-1, -2), (-2, 0), (-3, -2) ).

Please compare this information with the options you have to select the correct response based on these coordinates.