Question

What is the range of the function shown in the graph below? answer type: interval, all real values except one, all real values except two, all real numbers
Interval:

Answer 1

-4 to positive infinity

Answer 2

Answer: Interval from -4 to positive infinity

In interval notation, we write $[-4, \infty)$

This is the same as saying $y \ge -4$

The square bracket says "include -4 as part of the range" while the curved parenthesis says to exclude the endpoint of infinity. We can never reach infinity, so we can't include it as part of the real number line. Infinity is more of a concept than a number.

The range is the set of all possible outputs, or y values. In this case, we look at the lowest point to get the smallest y value possible, which is y = -4. So y = -4 is in the range. Anything larger than y = -4 is also possible and part of the range.