You go to the store to buy icecream. The icecream comes in a cylindrical tub that has a diameter of 5 inches and is 4 inches tal
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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
To write this in interval notation, we would write 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
In interval notation, it would be written as 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