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10. Suppose f(x) is a continuous function with some data points in the table below. At least how many

times must f(x) = 2 on [-2,7]? Why?

10. Suppose f(x) is a continuous function with some data points in the table below-example-1

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According to Bolzano's theorem (also known as the intermediate value theorem), if a continuous function defined on the interval [a;b] takes two different values, then it takes any value between them.

It immediately follows from this theorem that this function takes the value 2 on the intervals [-2;0], [4;6] and [6;7], that is, three times.

Answer: f(x)=2 at least three times.

The screenshot shows an example of a continuous function that takes these values.

10. Suppose f(x) is a continuous function with some data points in the table below-example-1
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