Question

What are the domain and range of the function below?

Answer 1

`Domain=[0,\infty)`

`Range=(-\infty,4]`

Explanation:

We need to find the domain and range of the function.

Domain : It is the set of input values or x values. In a graph, domain of the function represented by the x-axis.

Range : It is the set of output values or y values. In a graph, range of the function represented by the y-axis.

From the given graph it is clear that it is defined for
`0\le x<\infty` and
`-\infty <y\le 4`.

We have closed circle at (0,4). It means, 0 is included in the domain and 4 is included in the range.

`Domain=[0,\infty)`

`Range=(-\infty,4]`

Therefore,
`Domain=[0,\infty)` and
`Range=(-\infty,4]`.

Answer 2

Domain ={0,infinity)

Range = (-infinity, 4]

Explanation:

Given a graph with curve which has y intercept 4.

It passes x axis at 4 and extends fully

The domain is the set of values x can take

In the graph horizontal axis is x axis.

Hence from the graph we see that x can take values from 4 including 4 upto infinity.

Hence domain is x>=4

For range, we consider the values of y as per graph.

WE find that y is not taking values >4

Hence Range = (-infty, 4]