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.
▼Click for Long Desc
A concave-down, decreasing curve labeled option 1 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 f left parenthesis x right parenthesis equals to square root of left parenthesis x minus 1 right parentesis 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 option 2 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 option 3 spans from left parenthesis 5 comma negative 3 right parenthesis to left parenthesis 1 comma negative 1 right parenthesis.

Given the graph of f(x)=x−1−−−−√+1
, which option shows the reflection of the graph about the origin?

(1 point)
The reflection of the graph of f(x)=x−1−−−−−√+1
about the origin is option
.

Answer 1

The reflection is option 2.

Reason: Reflecting about the origin maps (x,y) to (−x,−y), so (1,1)→(−1,−1) and (5,3)→(−5,−3). The reflected curve is concave-up and increasing on [−5,−1], which matches option 2.