|
Question 128568: Find the domain and range of the following:
c) 
d) 
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! c)
Looking at , we can see that there are no square roots, logs, and other functions where there are restrictions on the domain.
Also, we can see that the function does not have a division by x (or any combination of variables and constants).
So we don't have to worry about division by zero.
Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any in for x
So the domain of the function in set-builder notation is:
In plain English reads: x is the set of all real numbers (In other words, x can be any number)
Also, in interval notation, the domain is:
)
Now to find the range, simply graph the function to get
From the graph, we can see that the lowest point is (0,0). So the smallest that y can be is 0
So the range of the function in set-builder notation is:
In plain English reads: y is the set of all real numbers that are greater than or equal to 0
Also, in interval notation, the range is:
[0, )
d)
Looking at , we can see that there are no square roots, logs, and other functions where there are restrictions on the domain.
Also, we can see that the function does not have a division by x (or any combination of variables and constants).
So we don't have to worry about division by zero.
Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any in for x
So the domain of the function in set-builder notation is:
In plain English reads: x is the set of all real numbers (In other words, x can be any number)
Also, in interval notation, the domain is:
Now to find the range, simply graph the function to get
From the graph, we can see that the lowest point is (-2,0). So the smallest that y can be is 0
So the range of the function in set-builder notation is:
In plain English reads: y is the set of all real numbers that are greater than or equal to 0
Also, in interval notation, the range is:
[0,)
|
|
|
| |
