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

(1 point)
Responses

Option 3
Option 3

Option 4
Option 4

Option 2
Option 2

Option 1

1 answer

To find the graph of \(-f(x)\), we first need to understand that \(-f(x)\) is the reflection of \(f(x)\) across the x-axis.

The given function is \(f(x) = x + 1\), which is a straight line with a slope of 1 that intersects the y-axis at (0, 1).

To find \(-f(x)\):

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

This means that the new line will have a slope of -1 and will intersect the y-axis at (0, -1).

Now, we can determine which option reflects this transformation.

  1. Look for a line with a negative slope (downward slope) that crosses the y-axis at (0, -1).
  2. Given that I don't have access to the options directly, compare the properties of the options provided.

In summary:

  • The line representing \(-f(x)\) will slope downwards from left to right and intersect the y-axis at (0, -1). Make sure to choose the option that meets these criteria. If you have images or descriptions of the options, you can identify the correct one based on these observations.