Question

For each of the following relations, identify whether it's a function or not and why, then state the domain

and range.
a) (0 , 5) , (1 , 9) , (2 , 13) , (1 , 20)
b) y = 3x + 8
c) y = x^2 + 1"

Answer 1

The relation in a) is not a function due to duplicate x-values. Equation b) and c) are functions with different domains and ranges.

Step-by-step explanation:

The relation is not a function because it contains duplicate x-values. In this case, the x-value 1 is associated with both the y-values 9 and 20. A function must have only one y-value for each x-value. The domain of the relation is {0, 1, 2} and the range is {5, 9, 13, 20}.

For equation b) y = 3x + 8, it is a function because for every x-value, there is only one corresponding y-value. The domain is all real numbers and the range is all real numbers.

For equation c) y = x^2 + 1, it is also a function because for every x-value, there is only one corresponding y-value. The domain is all real numbers and the range is y is greater than or equal to 1.