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)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%5Cinfty%29)
And in set notation, this is:
![\{x|x\in\mathbb{R}\}](https://tex.z-dn.net/?f=%5C%7Bx%7Cx%5Cin%5Cmathbb%7BR%7D%5C%7D)
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]](https://tex.z-dn.net/?f=%28-%5Cinfty%2C-4%5D)
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}\}](https://tex.z-dn.net/?f=%5C%7By%7Cy%5Cin%5Cmathbb%7BR%7D%2Cy%5Cleq%204%7D%5C%7D)