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The piecewise-function 𝑓(𝑥) has opposite expressions. 𝑓(𝑥)={2𝑥−1,𝑥<00,𝑥=0−2𝑥+1,𝑥>0Which is the graph of 𝑓(𝑥)

Question

The piecewise-function 𝑓(𝑥) has opposite expressions.

f(x)={2x−1,x<00,x=0−2x+1,x>0 f(x) = \begin{cases} 2x - 1, & x < 0 \\ 0, & x = 0 \\ -2x + 1, & x > 0 \end{cases}

Which is the graph of 𝑓(𝑥)?

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Solution

The graph of the function f(x) would be a straight line with a slope of 2 and y-intercept of -1 for x<0, a single point at (0,0) for x=0, and a straight line with a slope of -2 and y-intercept of 1 for x>0.

Here are the steps to graph the function:

  1. Draw a straight line with a slope of 2 and y-intercept of -1. This line should extend from the y-intercept to the left, stopping at x=0.

  2. Plot a single point at (0,0).

  3. Draw a straight line with a slope of -2 and y-intercept of 1. This line should extend from the y-intercept to the right, starting at x=0.

Remember, the lines for x<0 and x>0 should not cross the y-axis. The point at x=0 is the only part of the graph on the y-axis.

This problem has been solved

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