Intermediate Value Theorem

If a function f has a domain

 $\left(-\infty,\ \infty\right)$  , then it is _______________.

• increasing

• extraneous

• continuous

• undefined

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.5

For the function

 $f\left(x\right)=\lfloor x\rfloor$  , determine an interval where f is continuous.

• [0.5, 1.5]

• [-1, 1]

• [-2, 0]

• [1, 1.5]

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.4

CCSS.HSF.IF.B.5

CCSS.HSF.IF.C.7

Suppose t is a continuous function containing the ordered pairs shown in the table. On which interval(s) must t attain a value of -2.5? Select all that apply.

• (1, 2)

• (2, 3)

• (3, 4)

• (4, 5)

• (5, 6)

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Suppose f is a continuous function containing the ordered pairs shown in the table. On which interval(s) must f attain a value of 5.9? Select all that apply.

• (-3, -2)

• (-2, -1)

• (0, 1)

• (1, 2)

• (2, 3)

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Suppose h is a continuous function containing the ordered pairs shown in the table. On which interval must h have a zero?

• (12.163, 12.164)

• (12.164, 12.165)

• (12.165, 12.166)

• (12.166, 12.168)

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.11

Assume f(x) is continuous over the interval [-2, 3]. The function f has at least how many zeros?

• 1

• 2

• 3

• 4

Tags

CCSS.HSA.APR.B.3

Determine the interval(s) for which the function is continuous. Select all that apply.

• (p, 0)

• [0, q]

• [q, r]

• (r, s)

• (q, s)

Tags

CCSS.HSF.IF.B.5

Use the Intermediate Value Theorem to find an interval between two consecutive integers that contains a zero of the function

 $h\left(x\right)=2x-x^2-\ln x$  

• [-1, 0]

• [0, 1]

• [1, 2]

• (-1, 1)

Tags

CCSS.HSA.REI.D.11

Consider the function

 $f\left(x\right)=\frac{1}{x-3}-5$  .  Can you conclude that there must be a zero between f(2) and f(3.1)?

• Yes, because f(2) is negative and f(3.1) is positive.

• No, because f(2) is negative and f(3.1) is also negative.

• Yes, because f(2) is positive and f(3.1) is negative.

• No, because there is a discontinuity at x = 3.

• No, because f(2) is positive and f(3.1) is also positive.

Tags

CCSS.HSA.REI.D.10

A hot apple pie is left on a window sill to cool. Suppose its temperature (degrees F) after x minutes is given by

 $f\left(x\right)=90e^{-0.61x}+70$  .  Give an interval in which its temperature will first be under  $100\degree F$  

• (0, 0.5)

• (0.5, 1)

• (1, 1.5)

• (1.5, 2)

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.D.11