Question

Use the image to answer the 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.

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

(1 point)
Responses

Option 4
Option 4

Option 2
Option 2

Option 1
Option 1

Option 3
Option 3
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Answer 1

To find the graph of \(-f(x)\) given \(f(x) = x + 1\), we need to apply a vertical reflection across the x-axis to the original graph of \(f(x)\). The resulting function will be:

\[
-f(x) = -(x + 1) = -x - 1
\]

This means the graph will be a straight line with a negative slope (specifically, -1) and a y-intercept at -1.

To identify which option corresponds to the graph of \(-f(x)\):

1. The slope will be -1, indicating that the line will tilt downwards from left to right.
2. The line will cross the y-axis at -1 instead of at +1.

Without seeing the actual options graphically, I cannot specify which option is correct. However, you should look for a straight line that:
- Is declining as it moves from left to right.
- Intersects the y-axis at (0, -1).

Once you find the option that matches these criteria, that will be the correct graph of \(-f(x)\).