Questions: Functions Graphing a piecewise-defined function: Problem type 1 Suppose that the function h is defined, for all real numbers, as follows. h(x) = -3 if x < -1 0 if x = -1 -1 if x > -1 Graph the function h.

Functions
Graphing a piecewise-defined function: Problem type 1

Suppose that the function h is defined, for all real numbers, as follows.

h(x) =
-3 if x < -1
0 if x = -1
-1 if x > -1

Graph the function h.

Transcript text: Functions Graphing a piecewise-defined function: Problem type 1 Suppose that the function $h$ is defined, for all real numbers, as follows. \[ h(x)=\left\{\begin{array}{cl} -3 & \text { if } x<-1 \\ 0 & \text { if } x=-1 \\ -1 & \text { if } x>-1 \end{array}\right. \] Graph the function $h$.

Solution

Solution Steps

Step 1: Understand the Piecewise Function

The function $ h(x) $ is defined as: \[ h(x) = \begin{cases} -3 & \text{if } x \leq -1 \\ 0 & \text{if } x = -1 \\ -1 & \text{if } x > -1 \end{cases} \]

Step 2: Plot the First Segment

For $ x \leq -1 $, $ h(x) = -3 $. This is a horizontal line at $ y = -3 $ for all $ x \leq -1 $.

Step 3: Plot the Second Segment

For $ x = -1 $, $ h(x) = 0 $. This is a single point at $ (-1, 0) $.

Step 4: Plot the Third Segment

For $ x > -1 $, $ h(x) = -1 $. This is a horizontal line at $ y = -1 $ for all $ x > -1 $.