Check the picture below.
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What is the difference between -5 and 3?
2 answers:
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<h3>Domain: (-5, 3]</h3><h3>Range: [-4, 5)</h3>
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Explanation:
The domain is the set of allowed x values. In terms of a graph, we look at the left most point to see that x = -5 is the smallest x value possible. However, there's an open hole at this endpoint, so -5 itself is actually not part of the domain. So x must be larger than -5. At the same time, x can be as large as x = 3. Look at the very right tip of the graph to find this x value.
So x spans from -5 to 3, excluding -5 but including 3. We would write which converts to the interval notation (-5, 3]. Note the mix of curved parenthesis and square bracket. The curved parenthesis means to exclude the endpoint, while the square bracket means include the endpoint.
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The range is the set of possible y outputs. Find out the lowest point of the graph. That is when y = -4 and this value is included due to the filled in circle at the endpoint. But we do not include the largest y value y = 5 as there's an open hole at this endpoint.
So the range is the set of y values such that which in interval notation would be written as [-4, 5)
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So in short, you're looking for the min and max of x and y to get the domain and range respectively. Be sure to exclude any values where there are open holes as those do not count as part of the graph.