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 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 of the options is the graph of f(−x)
?

(1 point)
The graph of f(−x)
is option
.

Answer 1

Option 1.

Reason: f(-x) is the y-axis reflection of f(x), so (1,1) → (-1,1) and (5,3) → (-5,3). The reflected curve is concave down and decreasing on [-5,-1], which matches option 1.