Question

Four lines with bidirectional arrows are plotted and labeled on a coordinate plane. The equation f left parenthesis x right parenthesis equals x plus 1 appears at the top of the graph in quadrant 1.
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The values on both axes range from negative 4 to 4 in increments of 1. The dotted line, labeled Option 1, begins in quadrant 3 sloping upward from left to right, passes through quadrant 4, and then rises through quadrant 1. The dotted line passes through left parenthesis negative 3 comma negative 4 right parenthesis and left parenthesis 4 comma 3 right parenthesis. The dashed line, labeled Option 2, begins in quadrant 2 sloping downward from left to right, passes through quadrant 3, and then descends through quadrant 4. The dashed line passes through left parenthesis negative 4 comma 3 right parenthesis and left parenthesis 3 comma negative 4 right parenthesis. The dot-dashed line, labeled Option 3, begins in quadrant 2 sloping downward from left to right, passes through quadrant 1, and then descends through quadrant 4. The dot-dashed line passes through left parenthesis negative 3 comma 4 right parenthesis and left parenthesis 4 comma negative 3 right parenthesis. The solid line, labeled Option 4 f left parenthesis x right parenthesis equals to x plus 1, begins in quadrant 3 sloping upward from left to right, passes through quadrant 2, and then rises through quadrant 1. The solid line passes through left parenthesis negative 4 comma negative 3 right parenthesis and left parenthesis 3 comma 4 right parenthesis.

Given the graph of f(x)=x+1
, which of the options is the graph of −f(x)
?

(1 point)
Responses

Option 1
Option 1

Option 3
Option 3

Option 2
Option 2

Option 4

Answer 1

Option 2.

Reason: -f(x) = -(x+1) = -x - 1, a line with slope -1 and y-intercept -1. It is the reflection of f(x) across the x-axis, so the points (-4,-3) and (3,4) become (-4,3) and (3,-4), which matches Option 2.