Calc 12 ch 2.3 Intermediate value theorem

• increasing

• extraneous

• continuous

• undefined

• [0.5, 1.5]

• [-1, 1]

• [-2, 0]

• [1, 1.5]

Tags

CCSS.HSF-IF.C.7B

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

• 1

• 2

• 3

• 4

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.8.F.A.1

CCSS.HSF.IF.B.5

• [-1, 0]

• [0, 1]

• [1, 2]

• (-1, 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.

• (0, 0.5)

• (0.5, 1)

• (1, 1.5)

• (1.5, 2)

Let f be a continuous function for which f(-2)=1 and f(5)=-3. The Intermediate Value Theorem guarantees that

• f(c)=2 for at least one c between -3 and 1

• f(c)=0 for at least one c between -2 and 5

• f(c)=0 for at least one c between -3 and 1

• f(c)=2 for at least one c between -2 and 5

TRUE OR FALSE?  If f is continuous on [-1,1], f(-1)=4 and f(1)= -2, then there is a zero between -1 and 1.

• TRUE
• FALSE
• CANNOT BE DETERMINED

• TRUE because there is a sign change on the interval

• FALSE because there is no sign change on the interval

• TRUE because of the Intermediate Value Theorem

• FALSE because the function is discontinuous on the interval