Question

Use the image to answer the question.

Four concave curves are drawn on a coordinate plane with the x-axis from negative 6 to 6 and the y-axis from negative 4 to 4, both in increments of 2.
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A concave-down, decreasing curve labeled graph B spans from left parenthesis negative 5 comma 3 right parenthesis to left parenthesis negative 1 comma 1 right parenthesis. A concave-down, increasing curve labeled graph A and also f left parenthesis x right parenthesis equals to square root of left parenthesis x minus 1 right parenthesis plus 1, spans from left parenthesis 1 comma 1 right parenthesis to left parenthesis 5 comma 3 right parenthesis. A concave-up, increasing curve labeled graph C spans from left parenthesis negative 5 comma negative 3 point 5 right parenthesis to left parenthesis negative 1 comma negative 1 right parenthesis. A concave-up, decreasing curve labeled graph D spans from left parenthesis 5 comma negative 3 right parenthesis to left parenthesis 1 comma negative 1 right parenthesis.

Given the graph of y=f(x)
, which of the following options is the graph of y=−f(x)
? Enter the option number of the correct answer.

Option #1: Graph B

Option #2: Graph C

Option #3: Graph D

(1 point)

Answer 1

Option 3

Reflection across the x-axis sends (1,1)→(1,−1) and (5,3)→(5,−3), reversing sign and concavity. That matches graph D (concave-up, decreasing from (1,−1) to (5,−3)).