3.4 Intermediate Value Theorem

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

Given a continuous function on the interval [4,7].  Let's say that f(4) = 10 and f(7) = 20.  Is there a value on the interval [4,7] where f(x) = 15?

• Yes - if the function is continuous, then there must be an x value on that interval that passes through 15 on its way from 10 to 20.
• No because there is no sign change on the interval [4,7].
• No because that would be just too good to be true.
• Yes - at x = 5.5.

Tags

CCSS.HSA.REI.D.11

There is a hole in the graph

• when the numerator and denominator have a common factor
• where the denominator equals zero
• if the degree of the numerator is exactly one more than the denominator
• if the degree of the numerator and denominator are the same.

there is a vertical asymptote

• when the denominator equals zero
• when the degree of the numerator is exactly one more than the denominator
• when there is a common factor in the numerator and denominator
• when the degree of the numerator is the same as the denominator

Which of the following best describes the continuity at x = 5?

• Maximum

• Minimum

• Vertical Asymptote

• Hole

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10

Find the vertical asymptotes and holes of
y = (x+3) / (x-1)(x+3)

• Holes: None;
  VA: x = 1, -3
• Holes: x = -3;
  VA: x = 1
• Holes: x = -3, 1
  VA: None
• Holes: x = 1
  VA: x = -3

Tags

CCSS.HSA.APR.B.3