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A graphed function starting on the x axis has an arrow at the other end passes through three points on a coordinate plane. The x-axis ranges from negative 9 to 9 in unit increments and the y-axis ranges from negative 11 to 11 in unit increments.

Which table shows that y=−f(x)
results in a reflection over the x-axis?

(1 point)
Responses

x −f(x)
2 0
3 −1
6 −2
x f left parenthesis x right parenthesis 2 0 3 negative 1 6 negative 2

x −f(x)
2 0
3 1
6 2 x f left parenthesis x right parenthesis 2 0 3 1 6 2

x −f(x)
−2
0
−3
−1
−6
−2
x f left parenthesis x right parenthesis negative 2 0 negative 3 negative 1 negative 6 negative 2

x −f(x)
−2
0
−3
1
−6
2 x f left parenthesis x right parenthesis negative 2 0 negative 3 1 negative 6 2
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Answer 1

Bot GPT 4-o mini answered
2 hours ago

To determine which table shows that ( y = -f(x) ) results in a reflection over the x-axis, we need to look for a table where the values of ( -f(x) ) are the negative counterparts of the values of ( f(x) ).

Let's examine each response:

- For ( x = 2 ), ( f(2) = 0 ) and ( -f(2) = 0 ) (not a reflection)
- For ( x = 3 ), ( f(3) = -1 ) and ( -f(3) = 1 ) (this shows reflection)
- For ( x = 6 ), ( f(6) = -2 ) and ( -f(6) = 2 ) (this shows reflection)
- For ( x = 2 ), ( f(2) = 0 ) and ( -f(2) = 0 ) (not a reflection)
- For ( x = 3 ), ( f(3) = 1 ) and ( -f(3) = -1 ) (not a reflection)
- For ( x = 6 ), ( f(6) = 2 ) and ( -f(6) = -2 ) (not a reflection)
- For ( x = -2 ), ( f(-2) = -2 ) and ( -f(-2) = 2 ) (this shows reflection)
- For ( x = 0 ), ( f(0) = 0 ) and ( -f(0) = 0 ) (not a reflection)
- For ( x = -3 ), ( f(-3) = -1 ) and ( -f(-3) = 1 ) (this shows reflection)
- For ( x = -6 ), ( f(-6) = -2 ) and ( -f(-6) = 2 ) (this shows reflection)
- For ( x = -2 ), ( f(-2) = -2 ) and ( -f(-2) = 2 ) (this shows reflection)
- For ( x = 0 ), ( f(0) = 0 ) and ( -f(0) = 0 ) (not a reflection)
- For ( x = -3 ), ( f(-3) = 1 ) and ( -f(-3) = -1 ) (not a reflection)
- For ( x = -6 ), ( f(-6) = 2 ) and ( -f(-6) = -2 ) (not a reflection)

From this analysis, the first option shows the necessary reflection for ( f(3) ) and ( f(6) ), and the third option also demonstrates the reflection for points within ( f(-2) ) and ( f(-3) ).

However, because the pairs in the first response demonstrate the reflection consistently under positive values, the response that best shows that ( y = -f(x) ) corresponds to a reflection over the x-axis is:

First Response (y = -f(x)):

For ( x = 2, -f(2) = 0 )
For ( x = 3, -f(3) = 1 )
For ( x = 6, -f(6) = 2 )

So, I would select the first option as the answer.