How to find domain in interval notation on a graph

Asked by admin @ 10/11/2021 in Mathematics viewed by 317 People

What is the domain and range of the graph below? You must use either interval notation or set notation

Answered by admin @ 10/11/2021

Answer:

See below.

Step-by-step explanation:

The domain of a function is simply the span of x-values the graph will encompass.

And the range of a function is simply the span of y-values the graph will encompass.

Since the function is a quadratic, the domain is all real numbers. From the graph, the graph will continue to expand left and right. Therefore, the domain is all real numbers.

In interval notation, this is:

$(-\infty,\infty)$

And in set notation, this is:

$\{x|x\in\mathbb{R}\}$

For the range, notice that the graph is going downwards. In other words, the graph has a maximum value. From the graph, we can see that this maximum value is at y=-4. The graph never reaches any value above -4. Therefore, our range is all numbers equal to or less than -4.

In interval notation, this is:

$(-\infty,-4]$

We use brackets because we include the -4 in the solution set.

Also, note that we write the infinity first because the smallest number should be on the left. [-4, -∞) would not be correct.

And in set notation, this is:

$\{y|y\in\mathbb{R},y\leq 4}\}$

How to find domain in interval notation on a graph

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