Question

Graph the function f(x)={x+1ifx<0}
Real equation |
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on the coordinate plane.

Answer 1

Answer: The graph is shown below

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Explanation:

This piecewise function

$f(x) = \begin{cases}x+1 \ \ \text{ if } x < 0\\2 \ \ \ \ \ \ \ \text{ if } 0 \le x \le 1\\x \ \ \ \ \ \ \ \text{ if } x > 1\\\end{cases}$

is the same as saying...

• when x < 0, f(x) = x+1
• when $0 \le x \le 1$, f(x) = 2
• or when x > 1, f(x) = x

All three of those statements combine to form the piecewise function.

In other words, f(x) has a split personality. It depends on what x is that will determine what f(x) is. To graph this, we graph the pieces of y = x+1, y = 2 and y = x based on the restrictions for x above.

• The first piece y = x+1 is graphed when x < 0
• The second piece y = 2 is graphed when $0 \le x \le 1$
• The third piece y = x is graphed when x > 1

The graph is shown below. Note the use of open holes vs closed circle endpoints (indicating which points are not part of the graph vs those that are). The closed endpoints happen when the inequality sign has a "or equal to" as part of it; otherwise, we'll have an open endpoint.