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

(1 point)
Responses

Option 1
Option 1

Option 4
Option 4

Option 2
Option 2

Option 3

Answer 1

To find the graph of \(-f(x)\), we need to consider the effect of negating the function. The original function is:

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

When we negate the function, we have:

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

This means the graph of \(-f(x)\) will be a line that slopes downwards (since the coefficient of \(x\) is negative) and has a y-intercept of -1.

The general characteristics of the graph of \(-f(x) = -x - 1\) are:

• It crosses the y-axis at (0, -1).
• It has a slope of -1.

To identify the correct option for the graph of \(-f(x)\), look for the graph that:

1. Crosses the y-axis at -1 (0, -1).
2. Slopes downward from left to right.

Without the specific graph options available, you would look for these characteristics in the provided options to determine which one accurately represents \(-f(x)\).

Please check the options and select the one that has these features. If you can provide me with a description of each option, I can help you further narrow it down.