1. The given function is:
![g(x)=\begin{cases}5-x,-1\le x\le2 \\ x^2-1,2This is a piecewise function, the first part is given in the interval [-1,2], then let's solve this part for x=-1,0,1,2:<p>x=-1</p>[tex]g(-1)=5-(-1)=5+1=6]()
x=0

x=1

x=2

Now, the second part is given in the interval (2,3]
Then let's solve for x=2.01 and x=3:
x=2.01

x=3:

Now, we can graph these ordered pairs:
This function is continuous on the interval [-1,3].
2. The given function is:

The first part of the function is given in the interval [-1,3).
Let's find f(x) for x=-1,0,1,2,2.99
x=-1

x=0

x=1

x=2

x=2.99

The second part is given in the interval [3,5]
Then let's find f(x) for x=3,4,5
x=3

x=4

x=5

Now, we can graph the function by graphing these ordered pairs:
The function is continuous in the interval [-1,5]