Question

graph the following function on the axes provided.
$f(x)=\

$$\begin{cases}x + 7&\\text{for}\\\\x + 4&\\text{for}\\ - 1 < x \\leq 3\\end{cases}$$

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

Explanation:

Step1: Analyze the first piece \( y = x + 7 \)

Assume the domain for \( y = x + 7 \) is \( x \leq - 1 \) (since the second piece starts at \( x > - 1 \)). Find two points:

• When \( x=-1 \), \( y=-1 + 7=6 \). So the point is \( (-1,6) \) (closed dot as \( x = - 1 \) is included in this piece).
• When \( x=-2 \), \( y=-2 + 7 = 5 \). So the point is \( (-2,5) \).

Step2: Analyze the second piece \( y=x + 4 \)

The domain is \( - 1

• When \( x=-1 \), \( y=-1 + 4 = 3 \) (open dot as \( x=-1 \) is not included in this piece).
• When \( x = 3 \), \( y=3 + 4=7 \) (closed dot as \( x = 3 \) is included).
• Another point: when \( x = 0 \), \( y=0 + 4=4 \), point \( (0,4) \).

To graph:

• For \( y=x + 7 \) (domain \( x\leq - 1 \)): draw a line through \( (-2,5) \) and \( (-1,6) \) with a closed dot at \( (-1,6) \).
• For \( y=x + 4 \) (domain \( - 1

Answer:

The graph consists of two line segments: one for \( y = x+7 \) (with \( x\leq - 1 \)) passing through \((-2,5)\) and \((-1,6)\) (closed at \((-1,6)\)) and one for \( y=x + 4 \) (with \(-1