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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 2
Option 2

Option 3
Option 3

Option 4
Option 4
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1 answer

To find the graph of \(-f(x)\) for the function \(f(x) = x + 1\), we first need to understand that \(-f(x)\) will be the reflection of \(f(x)\) over the x-axis.

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

  2. To find \(-f(x)\), multiply the entire function by -1: \[ -f(x) = -(x + 1) = -x - 1 \]

  3. The graph of \(-x - 1\) will:

    • Have a negative slope (downward-sloping line).
    • Cross the y-axis at -1 (the y-intercept).

Now, you would look for a graph that has these characteristics:

  • A line that slopes downwards from left to right.
  • A y-intercept at -1.

Since I don’t have access to the actual options, you will want to choose the option that matches the characteristics of the line \(-x - 1\). If you have more specific details about the options available, I can further help narrow it down.