Question

Can someone help with algebra 2?

Answer 1

The given function is

$f(x)=\begin{cases}\frac{1}{3}x+1\colon x$

A piecewise function is a function that behaves differently on each interval. In this case, we have three intervals with three different behaviors, so let's graph each of them.

First part. 1/3x + 1.

We have to find coordinated points for the values x = -4 and x = -3. To do so, we have to evaluate the expression for each value.

$\begin{gathered} \frac{1}{3}\cdot(-4)+1=-\frac{4}{3}+1=\frac{-4+3}{3}=-\frac{1}{3} \\ \frac{1}{3}\cdot(-3)+1=-1+1=0 \end{gathered}$

So we have two points for the first expression: (-4, -1/3) and (-3, 0).

Second part. x - 3.

Let's evaluate the expression for x = -1 and x = 0.

$\begin{gathered} -1-3=-4 \\ 0-3=-3 \end{gathered}$

The points are (-1, -4) and (0, -3).

For the third part, we don't have to evaluate any expression because the function, in that interval, is a horizontal line.

Now, we just have to graph all the points on the same coordinated plane, as the image below shows.