Question

it says I'm supposed to graph each function and then right down the domain and range. I'm a remote student and I have no idea where to start on this

Answer 1

Notice that this function is defined in two parts (piecewise function) depending on the value of the variable "x".

So first thing is to find on the x-axis of the graph the point at which the function changes denominations. Those points are x = -1, and x = 1 since notice that for x smaller than -1 you need to use the constant value "3' for the function, while for x larger than 1 (to the right of that value) you need to use the expression of a line "x + 1" which has slope "1" (one) and y-intercept "1" (one). In the middle, there is no definition for the function.

Therefore we are going to mark on the graph a division and expect different graphs to appear to the left and to the right of the x = -1, and to the left and right of "1":

Notice that to the left of x = -1 we have plotted a horizontal line which corresponds to a constant value of "3" units on the y-axis. Notice as well a little "empty circe" at the location where the x is -1 (this is because we cannot include the point f(-1), given that the funcyion is not defined there.

Now, to the right of x = 1 we have the line with slope 1 and which (if allowed) would cross the y-axis at y = 1. Notice as well a little "empty circle" for the value x=1 since the function is not defined at that point.

Now, the Domain consists of all x-values to the left of -1, Union all the x-values to the right of 1. This in interval notation is noted as:

`\begin{gathered} (-\infty,-1)\cup(1,\infty) \\ \text{Domain}=\mleft\lbrace x\mright|x<-1\text{ or x>1}\} \end{gathered}`

Then the Range is the set of all y-values reached by the x values of the domain, so in our case, this set consists of all y values larger than 2. which in set builder notation is written as:

`\text{Range}=\mleft\lbrace y\mright|y>2\}`

Pasting Image of Domain and Range below since user reports viewing problems: