graph the following function on the axes provided.

$f(x)=\begin{cases}x + 1&\text{for}&-4

Question

graph the following function on the axes provided.

$f(x)=\begin{cases}x + 1&\text{for}&-4<x\leq0\\-5&\text{for}&0<x\leq3\end{cases}$

click and drag to make a line. click the line to delete it.
click on an endpoint of a line to change it.

Accepted Answer

# Explanation:
## Step1: Analyze the first part of the piece - wise function
For $y = x + 1$ where $-4\lt x\leq0$.
When $x=-4$, $y=-4 + 1=-3$ (but since $x\gt - 4$, this is an open - circle). When $x = 0$, $y=0 + 1=1$ (closed - circle).
## Step2: Analyze the second part of the piece - wise function
For $y=-5$ where $0\lt x\leq3$. When $x = 0$, $y=-5$ (open - circle) and when $x = 3$, $y=-5$ (closed - circle).

# Answer:
To graph the function $f(x)$:
1. For $y=x + 1$ ($-4\lt x\leq0$):
   - Plot an open - circle at the point $(-4,-3)$ and a closed - circle at the point $(0,1)$. Then draw a straight line connecting these two points (with the open - circle at $x=-4$).
2. For $y =-5$ ($0\lt x\leq3$):
   - Plot an open - circle at the point $(0,-5)$ and a closed - circle at the point $(3,-5)$. Then draw a horizontal line connecting these two points (with the open - circle at $x = 0$).

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QUESTION IMAGE

Question

Explanation:

Step1: Analyze the first part of the piece - wise function

Step2: Analyze the second part of the piece - wise function

Answer: