Use the image to answer the question.

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 option is the graph of f(−x)
?

(1 point)
Responses

The graph of f(−x)
is option 4.
The graph of f left parenthesis negative x right parenthesis is option 4.

The graph of f(−x)
is option 3.
The graph of f left parenthesis negative x right parenthesis is option 3.

The graph of f(−x)
is option 1.
The graph of f left parenthesis negative x right parenthesis is option 1.

The graph of f(−x)
is option 2

Answer 1

To determine the graph of \( f(-x) \) from the original function \( f(x) = x + 1 \), we need to understand how transformations work.

The function \( f(x) = x + 1 \) is a straight line with a slope of 1, which intercepts the y-axis at 1.

When we replace \( x \) with \( -x \) in the function, we get:

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

This represents a reflection of the original function \( f(x) \) across the y-axis. The slope becomes -1, meaning that the line will slope downwards rather than upwards.

Thus, the point (0, 1) remains unchanged, while points like (1, 2) would correspond to (-1, 2) in the transformed function.

To identify which option represents \( f(-x) \), you should look for a line that:

1. Intercepts the y-axis at (0, 1).
2. Slopes downwards to the right.

If you can refer to the given options, the correct response for the graph of \( f(-x) \) will be the one that represents the downward sloping line with the y-intercept at 1.

Based on these characteristics, please choose the option that correctly depicts these features from the given graph options.