Question Video: Determining the Range of a Piecewise Function from Its Graph | Nagwa Question Video: Determining the Range of a Piecewise Function from Its Graph | Nagwa

Question Video: Determining the Range of a Piecewise Function from Its Graph Mathematics • Second Year of Secondary School

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Determine the range of the function represented by the given graph.

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Video Transcript

Determine the range of the function represented by the given graph.

In this question, we’re given a graph of a function. And we need to use this graph to determine the range of this function. So let’s begin by recalling what we mean by the range of a function. It’s the set of all output values of the function given the domain of the function. So we need to use the graph of this function to determine all possible outputs of the function. We can do this by recalling when we graph a function, the 𝑥-coordinates of the points on the curve represent the input values of the function and the corresponding 𝑦-coordinates represent the output values.

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 𝑦-coordinates of points which lie on the curve. And we can find this directly from the given graph. For example, we can see there are many points on the graph of this function with 𝑦-coordinate seven. For example, if we call this the function 𝑓, we can see that the point with coordinates negative two, seven lies on the graph of this function. So 𝑓 evaluated at negative two must be equal to seven.

We can do the same for the other section of our graph. This section is also constant and all of the 𝑦-coordinates are negative seven. So we can see there are many points on this graph of 𝑦-coordinate negative seven. For example, the point with coordinates two, negative seven lies on the curve. So 𝑓 evaluated at two is equal to negative seven.

However, these are the only two possible 𝑦-coordinates of points which lie on the curve, since both parts of this graph remain constant at this value. We can see that these are just horizontal lines. Therefore, the range of this function only contains two values: negative seven and seven. We need to write this as a set. So it’s the set containing negative seven and seven.

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