Question

How do you find the domain and range of `10-x^2`?

Answer 1

See below.

Explanation:

Perhaps the best way to find domain and range is to look at a graph.
graph{10 - x^2 [-20, 20, -10, 10]}

There is, according to the graph, a y-intercept at (0,10), and this is the graph's maximum or highest point. Therefore, you know the range has to be:

y ≤ 10

Now, you want the domain. The graph continue's downward and across (left and right) until infinity. Therefore, the domain is:

x = ℝ (all real numbers)

I hope that helps!