Intermediate Value Theore

• 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

Tags

CCSS.HSA.REI.D.10

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 the function g(x) = 2x⁴ - x³ + 8/x which of the intervals must contain a zero?

• [-1,1]
• [0,2]
• [2,4]
• None of these intervals

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.11

TRUE OR FALSE?  There is a zero on the interval [1,3].

• True because the function is continuous and there is a sign change on the interval [1,3]
• We cannot be certain since the function is not continuous on the interval [1,3]
• False because there is no sign change on the interval [1,3]
• False because the graph is not continuous on the interval [1,3]

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

TRUE OR FALSE?  There is NO zero on the interval [-4,0].

• True - the function is not continuous on the interval
• True - there is no sign change on the interval [-4,0]
• False - the function is continuous and there is a sign change on the interval [-4,0]
• False - the IVT is an existence theorem.  It can tell us when we can be certain there IS a zero but not when to be certain when there is NOT.

Tags

CCSS.HSA.APR.B.3

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