# Function Continuity Flashcards

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*h*(

*x*) has a jump discontinuity at

*x*= 0.

*x*= 2.

*f*(

*x*) is continuous on the interval from

*a*to

*b*, then the function must take on every value between

*f*(

*a*) and

*f*(

*b*).

*x*-values where discontinuity occurs.

*f*(

*x*) is discontinuous at

*x*= 1.

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## Flashcard Content Overview

What makes a function continuous? And why do we need to know that it is continuous? This set of flashcards will help you review the properties of continuous functions and the Intermediate Value Theorem. You can also practice determining the various types of discontinuities that may occur in functions.

*x*-values where discontinuity occurs.

*f*(

*x*) is discontinuous at

*x*= 1.

*f*(

*x*) is continuous on the interval from

*a*to

*b*, then the function must take on every value between

*f*(

*a*) and

*f*(

*b*).

*x*= 2.

*h*(

*x*) has a jump discontinuity at

*x*= 0.

*f*(

*x*) = 5/(

*x*2 - 4).

*f*(

*x*) = 5/(

*x*2 - 4) is discontinuous at vertical asymptotes located at

*x*= -2 and

*x*= 2.

*g*(

*x*):

*g*(-1) = 5,

*g*(0) = 2, and

*g*(1) = -3. State the interval on which the function must have a root according to the Intermediate Value Theorem.

*g*(

*x*) must have a root on the interval from 0 and 1.

*f*(

*x*) = cos(3

*x*), consider the function values at

*x*=

*pi*/9,

*x*= 2

*pi*/9, and

*x*=

*pi*/3 (measured in radians.) Using those values, state the interval on which

*f*(

*x*) must cross the

*x*-axis.

*f*(

*x*) = cos(3

*x*) must cross the

*x*-axis on the interval from

*pi*/9 to

*2*pi

*/9.*

*f*(

*x*) has the following values:

*f*(-10) = -7 and

*f*(10) = 5. State the range of values that the function must take on in that interval.

*x*= 3 and an asymptotic discontinuity at

*x*= -3.

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Math 104: Calculus16 chapters | 135 lessons | 11 flashcard sets

- Go to Continuity

- Go to Series

- Go to Limits

- Graphing Functions Flashcards
- Function Continuity Flashcards
- Limits in Calculus Flashcards
- Rate of Change in Calculus Flashcards
- Solving Derivatives Flashcards
- Graphing Derivatives & L'Hopital's Rule Flashcards
- Applications of Derivatives Flashcards
- Integrals & the Area Under the Curve Flashcards
- Integration in Calculus Flashcards
- Differential Equations Flashcards
- Math 104: Calculus Formulas & Properties
- Go to Studying for Math 104