Suppose that the function f is defined as follows.

Questions: Suppose that the function f is defined as follows. f(x) = - -1 if -3 < x ≤ -2 - 0 if -2 < x ≤ -1 - 1 if -1 < x ≤ 0 - 2 if 0 < x ≤ 1 Graph the function f.

Transcript text: Suppose that the function $f$ is defined as follows. \[ f(x)=\left\{\begin{array}{cc} -1 & \text { if }-3

Solution

Solution Steps

Step 1: Plot the first piece of the function

For $-3 < x \le -2$, the function value is $f(x) = -1$. This is a horizontal line segment at $y=-1$ starting at $x=-3$ (open circle) and ending at $x=-2$ (closed circle).

Step 2: Plot the second piece of the function

For $-2 < x \le -1$, the function value is $f(x) = 0$. This is a horizontal line segment at $y=0$ starting at $x=-2$ (open circle) and ending at $x=-1$ (closed circle).

Step 3: Plot the third piece of the function

For $-1 < x \le 0$, the function value is $f(x) = 1$. This is a horizontal line segment at $y=1$ starting at $x=-1$ (open circle) and ending at $x=0$ (closed circle).

Step 4: Plot the fourth piece of the function

For $0 < x \le 1$, the function value is $f(x) = 2$. This is a horizontal line segment at $y=2$ starting at $x=0$ (open circle) and ending at $x=1$ (closed circle).

Final Answer:

The graph of the function $f(x)$ is a piecewise function consisting of four horizontal line segments.

         2 |----●
         1 |o----●
         0 |o----●
        -1 |o----●
         |
    -3 -2 -1  0  1
       x

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Questions: Suppose that the function f is defined as follows. f(x) = - -1 if -3 < x ≤ -2 - 0 if -2 < x ≤ -1 - 1 if -1 < x ≤ 0 - 2 if 0 < x ≤ 1 Graph the function f.

Solution

Solution Steps

Final Answer:

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