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.REI.D.11

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.2

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.REI.D.11

CCSS.HSA.APR.B.3

Which function would produce graph b?

• x^3/2
• x^4/3
• x^3/4
• x^2/3

Tags

CCSS.HSF-IF.C.7B

Which of the functions below would produce graph b?

• x^-1
• x^-2
• -x^-3
• -x^-4

Which of the functions below would produce graph c?

• x^-1
• x^-2
• -x^-3
• -x^-4

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.REI.D.11

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10