Question

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An upward, open parabola is plotted on a coordinate plane labeled in increments of 1. The x-axis ranges from 0 to 10. The y-axis ranges from 0 to 7.
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Given the function f(x)=(x−5)2+1
, determine g(x)
if it is a reflection of f(x)
over the x-axis.

(1 point)
Responses

g(x)=−(x−5)2+1
g left parenthesis x right parenthesis equals negative left parenthesis x minus 5 right parenthesis squared plus 1

g(x)=(−x−5)2+1
g left parenthesis x right parenthesis equals left parenthesis negative x minus 5 right parenthesis squared plus 1

g(x)=−(x+5)2−1
g left parenthesis x right parenthesis equals negative left parenthesis x plus 5 right parenthesis squared minus 1

g(x)=−(x−5)2−1
g left parenthesis x right parenthesis equals negative left parenthesis x minus 5 right parenthesis squared minus 1
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Answer 1

g(x) = −(x−5)^2 − 1

Reflection across the x-axis multiplies the y-value by −1: g(x) = −f(x) = −[(x−5)^2 + 1] = −(x−5)^2 − 1.