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 4
Option 4

Option 3
Option 3

Option 1
Option 1

Option 2

Answer 1

To determine which option represents the graph of \(-f(x)\) where \(f(x) = x + 1\), we need to understand how to graph the negative of a function.

1. Understand \(f(x) = x + 1\): This is a linear function with a slope of 1 and a y-intercept of 1. The graph is a straight line that passes through (0, 1) and rises at a 45-degree angle.

2. Determine \(-f(x)\): The equation for \(-f(x)\) becomes \(-f(x) = - (x + 1) = -x - 1\). This is also a linear function but with a slope of -1 and a y-intercept at -1.

3. Graph characteristics: The graph of \(-f(x)\) will be a straight line that:

   • Slopes downwards from left to right (due to the negative slope).
   • Crosses the y-axis at \(y = -1\) when \(x = 0\).

Given these characteristics, you should look for a straight line that goes through the point (0, -1) and slopes downwards.

Since I cannot see the options you mentioned, you will need to visually identify the line that fits this description among the options presented. It should be recognizable as a straight line that moves down from left to right, crossing the y-axis at -1.