Question

graph this function.
f(x)=\begin{cases}x + 3&\text{if }- 5<x<1\\2x&\text{if }1leq x<4end{cases}
select points on the graph to plot them. select \point fill\ to change a point from closed to open.

Explanation:

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

For \(f(x)=x + 3\) when \(-5Find the \(y\) - values for the endpoints:
When \(x=-5\), \(y=-5 + 3=-2\) (open - circle since \(x=-5\) is not in the domain).
When \(x = 1\), \(y=1 + 3=4\) (open - circle since \(x = 1\) is not in the domain).
We can also find other points, for example, when \(x=-2\), \(y=-2 + 3=1\).

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

For \(f(x)=2x\) when \(1\leq x<4\).
Find the \(y\) - values for the endpoints:
When \(x = 1\), \(y=2\times1 = 2\) (closed - circle since \(x = 1\) is in the domain).
When \(x = 4\), \(y=2\times4=8\) (open - circle since \(x = 4\) is not in the domain).
We can also find other points, for example, when \(x = 2\), \(y=2\times2=4\).

Step3: Plot the points

Plot the open and closed points from the above steps and draw the line segments for each part of the piece - wise function.

Answer:

Plot the points and draw the line segments as described above on the given coordinate grid. For \(y=x + 3\) with \(-5