Intermediate Value Theorem (IVT)

Intermediate Value Theorem (IVT)

Assessment

Flashcard

Mathematics

9th - 12th Grade

Practice Problem

Hard

CCSS
HSA.APR.B.3

Standards-aligned

Created by

Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Intermediate Value Theorem (IVT)?

Back

The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b], and takes on different values at the endpoints, then it must take on every value between f(a) and f(b) at least once within that interval.

2.

FLASHCARD QUESTION

Front

What does it mean for a function to be continuous on an interval?

Back

A function is continuous on an interval if there are no breaks, jumps, or holes in the graph of the function over that interval.

3.

FLASHCARD QUESTION

Front

If g is continuous on [-1, 4] and g(-1) = -4, g(4) = 1, what can we conclude using IVT?

Back

By the IVT, there exists at least one c in the interval [-1, 4] such that g(c) = -3.

4.

FLASHCARD QUESTION

Front

What is the significance of the endpoints in the IVT?

Back

The values of the function at the endpoints of the interval are crucial because they determine the range of values that the function must achieve within that interval.

5.

FLASHCARD QUESTION

Front

If h(x) is continuous on [1, 6] and h(3) = 0, what does this imply?

Back

It implies that there is a solution to h(x) = 0 at x = 3.

6.

FLASHCARD QUESTION

Front

What is an example of a function that satisfies the conditions of the IVT?

Back

An example is f(x) = x^2 - 4, which is continuous on any interval. For the interval [0, 4], f(0) = -4 and f(4) = 12, so by IVT, there exists c in [0, 4] such that f(c) = 0.

7.

FLASHCARD QUESTION

Front

What is the conclusion of the IVT if f(1) = 1 and f(5) = -3?

Back

The IVT guarantees that there exists at least one c in the interval [1, 5] such that f(c) = -2.

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