LT4 Intermediate Value Theorem

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.HSA.REI.D.11

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