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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 3
Option 3

Option 4
Option 4

Option 1
Option 1

Option 2
Option 2

1 answer

To find the graph of \(-f(x)\) based on the equation \(f(x) = x + 1\), we first note that \(-f(x) = -(x + 1) = -x - 1\).

The graph of \(-f(x)\) will be a straight line with a negative slope (-1) that crosses the y-axis at -1. This means it will slope downwards from left to right.

  1. The y-intercept of \(-f(x)\) is at the point (0, -1).
  2. The slope is -1, meaning for every unit you move to the right on the x-axis, you move down one unit on the y-axis.

When looking at the options provided (Options 1, 2, 3, and 4), look for a graph that:

  • Is a straight line,
  • Has a negative slope,
  • Crosses the y-axis at (0, -1).

Select the option that matches these characteristics.