Question

your friend needs to graph the piecewise function below but does not remember all the steps he or she needs to do here is what your friend has come up with please double check the work and correct any mistakes you find then explain why.

Answer 1

Graph of piece wise function in attachment.

Step-by-step explanation:

We are given a piece wise function.

`f(x)=\left\{\begin{matrix}3x-5 &\ \ \ \ \ \ \ \text{if}\ x\leq -1 \\ -2x+3 &\ \ \ \ \ \ \ \text{if}\ -1<x< 4 \\ 2 & \ \ \ \ \ \ \ \text{if}\ x\geq 4\end{matrix}\right.`

Here, we can see graph break at two points at x=-1 and x=4

We have to draw graph each piece function.

Part 1: When x≤-1

f(x)=3x-5

First point: (-1,-8) at this point draw dark circle because x is less than equal to -1.

Second Point: (-3,-14)

Now join both points and see the graph.

Part 2: when -1<x<4

f(x)=-2x+3

First point: (-1,5) and draw open circle.

Second point: (4,-5) and draw open circle.

Now join the both points and we get graph between interval (-1,4) or -1<x<4

Part 3: when x≥4

f(x)=4

It is constant function. It would be horizontal line start from (4,4) and go straight.