Use this to answer the question.

Question

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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GPT-4o mini · Answer

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: 1. - 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) 2. - 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) 3. - 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) 4. - 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.