Find the domain and range of the relation and determine whether it is a function.
a. domain: all real numbers; range: all real numbers; Yes, it is a function.

b. domain: positive integers; range: positive integers; No, it is not a function.

c. domain: x ≥ 0; range: y > 3; No, it is not a function.

d. domain: x > 3; range: y > 0; Yes, it is a function.

Hello there!

Let's look at the graph. If we do the vertical line test, we can figure out that YES, it is a function, so option b and c are already out of the picture.

Now, to find the domain, look at the graph and shade it back to the x-axis. The domain includes every number greater than 3, so the domain is x>3.

To find the range, take a look at the graph and shade it back to the y-axis. The range includes every real number greater than 0, so the range is y>0

This means that d is the answer.

I really hope this helps!
Best wishes :)

joaobezerra joaobezerra · Answer 2 · 2021-11-12T13:47:59+01:00

Using function concepts, it is found that the correct option is:

d. domain: x > 3; range: y > 0; Yes, it is a function.

A relation is a function if for each value of the input, there is only one respective value of the output. In a graph, it means that for each value of x, there is only one respective value of y.

In this graph, there is only one value of y for each value of x, hence, it is a function.

The domain of a function is the set that contains all possible input values. In a graph, it is the values assumed by x, the horizontal axis.

In this graph, x assumes values greater than 3, hence the domain is x > 3.

The range of a function is the set that contains all possible output values. In a graph, it is the values assumed by y, the vertical axis.

In this graph, y assumes values greater than 0, hence the range is y > 0.

A similar problem is given at https://brainly.com/question/10891721