# Suppose that f (x) is defined and continuous for all real number x and assume that f (x) takes on...

## Question:

Suppose that {eq}f (x) {/eq} is defined and continuous for all real number {eq}x {/eq} and assume that {eq}f (x) {/eq} takes on the following values: {eq}\displaystyle f (-2) = 6,\ f (0)= -3,\ f (2) = 4,\ f (3) = 0,\ f (4) = -1,\ f (7)= -3,\ \text{and}\ f (10) = 8 {/eq}. Give a list of non overlapping intervals in which solutions to the equation {eq}f (x) = 0 {/eq} can be found.

## Intermediate Value Theorem

We can draw a number of conclusions about a function if we know that it is continuous. One of these conclusions is stated in the Intermediate Value Theorem. This theorem states that if we know what a continuous function equals at the endpoints of an interval, we know that the function must equal every value in between these points at least once.

Since this function is defined to be continuous, we know that we can apply the Intermediate Value Theorem to it. One application of this theorem is...

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