Question

Find the domain and range of the function graphed in the picture.

Answer 1

The domain is the set of allowed x inputs, or x coordinates of a function. In this case, any point on the curve has an x coordinate that is 4 or smaller.

Therefore, the domain is the set of numbers x such that $x \le 4$

To write this in interval notation, we would write $(-\infty, 4]$ This interval starts at negative infinity and stops at 4. We exclude infinity with the curved parenthesis and include 4 with the square bracket.

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The range is the set of possible y outputs. Every point on this curve has a y coordinate that is either 0 or it is larger than 0.

The range is the set of y values such that $y \ge 0$

In interval notation, it would be written as $[0, \infty)$ This time we start at 0 (including this endpoint) and "stop" at infinity

note: we always use curved parenthesis at positive or negative infinity because we cannot reach either infinity