se 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 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.

1 answer

To find the graph of \( f(-x) \) from the original function \( f(x) = x + 1 \), we first replace \( x \) with \( -x \):

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

This means that the graph of \( f(-x) \) is obtained by reflecting the graph of \( f(x) \) across the \( y \)-axis.

The original graph \( f(x) = x + 1 \) is a straight line with a slope of 1 and a y-intercept at (0, 1). When we reflect this line across the y-axis, the slope becomes -1. Therefore, the new line \( f(-x) = -x + 1 \) will have a y-intercept at (0, 1) but will slope downwards.

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

  • Look for a straight line that also intersects the y-axis at \( (0, 1) \).
  • The line should descend from left to right (negative slope).

You can identify the correct option based on these characteristics. If you have the options visually or as a description, you can choose the one that matches the criteria listed above.

If you state what options 1-4 look like, I can help you determine which one corresponds to \( f(-x) \).