AP Calculus - IVT and Squeeze Theorem

• Yes because there is a sign change between x = -5 and x = 5

• No because there is a discontinuity between x = -5 and x = 5

• Yes because the Intermediate Value theorem applies

• No because there is no sign change between x = 5 and x = -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 OR FALSE?  If f(x) = |x+1|/(x+1), then there is a zero on the interval [-2,0].

• 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

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.2

CCSS.HSA.REI.D.11

Given the function f(x) = x³ + x - 3, which of the intervals below contains a zero?

• [-1,1]
• [0,1]
• [1,2]
• None of these intervals

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.11

Let f be a function that is continuous on the closed interval [2,4] with f(2) = 10 and f(4) = 20. Which of the following is guaranteed by the Intermediate Value Theorem?

• f(x) = 13 has at least one solution in the open interval (2,4)

• f(3) = 15

• f attains a maximum on the open interval (2,4)

• f(x) = 10 at some other value(s) of x other than x = 2

Tags

CCSS.HSA.REI.D.10

Let g be a function such that g(-1) = 0 and g(2) = 5. Which of the following conditions guarantee that there is an x, -1 < x < 2, for which g(x) = 3?

• g is defined for all x in (-1, 2)

• g is continuous for all x in [-1, 2]

• g is increasing on [-1, 2]

• there exists an x in (-1, 2) such that g(x) = 6

Tags

CCSS.HSA.REI.D.11

The table shows selected values of a continuous function f. For 0 ≤ x ≤ 13, what is the fewest possible number of times that f(x) = 4?

• One

• Two

• Three

• Four

Tags

CCSS.HSF.IF.B.4

Let f be a function that is continuous on the closed interval [1, 3] with f(1) = 10 and f(3) = 18. Which of the following statements MUST be true?

• 10 ≤ f(2) ≤ 18

• f is increasing on the interval [1, 3]

• f(x) = 17 has at least one solution in the interval [1, 3]

• f(2) = 14

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.B.5

CCSS.HSF.IF.C.7