Use the image to answer the question.

Question

Four lines each has option 1 2 3 4 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 2
Option 2

Option 3
Option 3

Option 4
Option 4

Option 1
Option 1

Answer 1

To find the graph of -f(x) given that f(x) = x + 1, we first need to determine what -f(x) looks like.

1. Start with the original function: \[ f(x) = x + 1 \]

2. Calculate -f(x): \[ -f(x) = -(x + 1) = -x - 1 \]

The graph of -f(x) = -x - 1 is a straight line with a slope of -1, which means it will slant downwards from left to right. The line crosses the y-axis at -1.

Now, you'll want to look at the options provided:

• The graph of -f(x) = -x - 1 will have:
  • A y-intercept of -1 (where it crosses the y-axis).
  • A slope of -1 (meaning it goes downwards to the right).

Without seeing the graph, you will need to identify the option that matches these characteristics. Look for the line that crosses the y-axis at -1 and has a downward slope.

If you can provide some description of each option’s characteristics, I can assist you in determining which option represents -f(x) = -x - 1.