WEBVTT
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Determine the range of the function represented by the given graph.
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In this question, weβre given a graph of a function.
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And we need to use this graph to determine the range of this function.
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So letβs begin by recalling what we mean by the range of a function.
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Itβs the set of all output values of the function given the domain of the function.
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So we need to use the graph of this function to determine all possible outputs of the function.
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We can do this by recalling when we graph a function, the π₯-coordinates of the points on the curve represent the input values of the function and the corresponding π¦-coordinates represent the output values.
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Therefore, since the range of the function is the set of all output values of the function, we can think about this as saying the set of all π¦-coordinates of points which lie on the curve.
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And we can find this directly from the given graph.
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For example, we can see there are many points on the graph of this function with π¦-coordinate seven.
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For example, if we call this the function π, we can see that the point with coordinates negative two, seven lies on the graph of this function.
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So π evaluated at negative two must be equal to seven.
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We can do the same for the other section of our graph.
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This section is also constant and all of the π¦-coordinates are negative seven.
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So we can see there are many points on this graph of π¦-coordinate negative seven.
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For example, the point with coordinates two, negative seven lies on the curve.
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So π evaluated at two is equal to negative seven.
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However, these are the only two possible π¦-coordinates of points which lie on the curve, since both parts of this graph remain constant at this value.
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We can see that these are just horizontal lines.
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Therefore, the range of this function only contains two values: negative seven and seven.
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We need to write this as a set.
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So itβs the set containing negative seven and seven.