suppose that the function f is defined as follows.\n f(x)=\begin{cases}-1&\text{if } - 2.5<xleq…

suppose that the function f is defined as follows.\n f(x)=\begin{cases}-1&\text{if } - 2.5<xleq - 1.5\\0&\text{if } - 1.5<xleq - 0.5\\1&\text{if } - 0.5<x<0.5\\2&\text{if }0.5leq x<1.5\\3&\text{if }1.5leq x<2.5end{cases}\ngraph the function f.

suppose that the function f is defined as follows.\n f(x)=\begin{cases}-1&\text{if } - 2.5<xleq - 1.5\\0&\text{if } - 1.5<xleq - 0.5\\1&\text{if } - 0.5<x<0.5\\2&\text{if }0.5leq x<1.5\\3&\text{if }1.5leq x<2.5end{cases}\ngraph the function f.

Answer

Explanation:

Step1: Analyze first - interval

For $-2.5 < x\leq - 1.5$, $f(x)=-1$. Draw a horizontal line segment at $y = - 1$ from $x=-2.5$ (open - circle) to $x = - 1.5$ (closed - circle).

Step2: Analyze second - interval

For $-1.5 < x\leq - 0.5$, $f(x)=0$. Draw a horizontal line segment at $y = 0$ from $x=-1.5$ (open - circle) to $x=-0.5$ (closed - circle).

Step3: Analyze third - interval

For $-0.5 < x<0.5$, $f(x)=1$. Draw a horizontal line segment at $y = 1$ from $x=-0.5$ (open - circle) to $x = 0.5$ (open - circle).

Step4: Analyze fourth - interval

For $0.5\leq x<1.5$, $f(x)=2$. Draw a horizontal line segment at $y = 2$ from $x = 0.5$ (closed - circle) to $x=1.5$ (open - circle).

Step5: Analyze fifth - interval

For $1.5\leq x<2.5$, $f(x)=3$. Draw a horizontal line segment at $y = 3$ from $x = 1.5$ (closed - circle) to $x=2.5$ (open - circle).

The graph consists of five horizontal line - segments with appropriate open and closed circles at the endpoints of each interval.

Answer:

The graph is a step - function with horizontal line segments at $y=-1$ for $-2.5 < x\leq - 1.5$, $y = 0$ for $-1.5 < x\leq - 0.5$, $y = 1$ for $-0.5 < x<0.5$, $y = 2$ for $0.5\leq x<1.5$ and $y = 3$ for $1.5\leq x<2.5$ with correct open and closed endpoints as described above.