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 (a y-value of zero) between -1 and 1.

• TRUE

• FALSE

• CANNOT BE DETERMINED

• 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

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

A function is ________ if there is a break in the function's graph.

• continuous
• open
• closed
• discontinuous

Tags

CCSS.8.F.A.3

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.

Tags

CCSS.HSF-IF.C.7D

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

Tags

CCSS.HSF-IF.C.7D

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

• Maximum

• Minimum

• Vertical Asymptote

• Hole

Tags

CCSS.HSF-IF.C.7D

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.HSF-IF.C.7D

INTERMEDIATE VALUE THEOREM
 $g\left(x\right)$  is continuous on  $\left[\ a,b\ \right]$  

 $k$  is between  $g\left(a\right)$  and  $g\left(b\right)$  

(check all that apply)

•  $k$  is a y-value :  $g\left(a\right)\ ,\ g\left(b\right)$  are x-values

•  $k\ ,\ g\left(a\right)\ ,\ g\left(b\right)$  are x-values

•  $k$  is an x-value :  $g\left(a\right)\ ,\ g\left(b\right)$  are y-values
  

•  $k\ ,\ g\left(a\right)\ ,\ g\left(b\right)$  are y values