Use a graph to find the range of the function y=f(x)=x^2-9 on the domain -4<=x<=5. Range?

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Answer 1

The range is the set of possibilities for what f(x) can be. If you draw a graph, you can use it to determine the range of f(x). Put values of f(x) on the y-axis. To find the points to be plotted and connected, make a table with two columns: x and f(x). For every integer, from -4 to 5, compute f(x), using that value of x. Find the lowest and highest resulting values of f(x). You can either look at the graph or your table to find them.

 

Here, the lowest value of f(x) is -9, when x = 0. The highest value of f(x) is 16, when x = 5. There are no gaps in the graph, so the range of f(x) is 0 ≤ f(x) ≤ 16.