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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 4
Option 4

Option 3
Option 3

Option 1
Option 1

Option 2
Option 2
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1 answer

To find the graph of \(-f(x)\) given that \(f(x) = x + 1\), we need to understand what \(-f(x)\) represents. The graph of \(-f(x)\) is obtained by reflecting the original graph of \(f(x)\) across the x-axis.

Here's how to determine this:

  1. Identify the original function: We have \(f(x) = x + 1\). This is a straight line with a slope of 1 and a y-intercept of 1. The line increases as x increases.

  2. Derive \(-f(x)\): \(-f(x) = -(x + 1) = -x - 1\). This means we have a line that has a slope of -1 and a y-intercept of -1. The line will decrease as x increases.

  3. Visual characteristics: The graph of \(-f(x)\) is a straight line that starts from the point (0, -1) and goes downwards to the right.

You should look for a graph that has these characteristics: it will start below the x-axis because of the negative y-intercept and will slope downwards.

If you have the options provided, look for a graph that:

  • Crosses the y-axis at -1 (that is, it intercepts the y-axis at the point (0, -1)).
  • Has a negative slope (the line should decrease from left to right).

Choose the option that matches this description.