Unit 1 Progress Check: MCQ Part B

The table above gives selected values for a function ff. Also shown is a portion of the graph of ff. The graph consists of a line segment for x<3x<3 and part of a parabola for x>3x>3. What is limx→3f(x)limx→3f(x) ?

A. 1.6

If ff is the function defined by f(x)=1x−1x−1f(x)=1x−1x−1, then limx→1f(x)limx→1f(x) is equivalent to which of the following?

A. limx→1(−1x)

The function gg is given by g(x)=7x−26x−5g(x)=7x−26x−5. The function hh is given by h(x)=3x+142x+1h(x)=3x+142x+1. If ff is a function that satisfies g(x)≤f(x)≤h(x)g(x)≤f(x)≤h(x) for 0<x<50<x<5, what is limx→2f(x)limx→2f(x) ?

B. 4

The function ff is defined above. Which of the following statements is true?

B. ff has a removable discontinuity at x=2x=2

Let f be the function defined above. Which of the following statements is true?

B. ff is not continuous at x=1x=1 because f(1)f(1) does not exist.

The graph of a function ff is shown in the figure above. At what value of xx does ff have a removable discontinuity?

B. x=3

The function ff has a jump discontinuity at x=3x=3. Which of the following could be the graph of ff ?

C

Let ff and gg be functions such that limx→4g(x)=2limx→4g(x)=2 and limx→4f(x)g(x)=πlimx→4f(x)g(x)=π. What is limx→4f(x)limx→4f(x) ?

C. 2π

Which of the following functions is continuous at x=3 ?

C. h(x)=⎧⎩⎨⎪⎪−8sin(π2x)8−8cos(πx)forx<3forx=3forx>3

Let ff be a function of xx. The value of limx→af(x)limx→af(x) can be found using the squeeze theorem with the functions gg and hh. Which of the following could be graphs of ff, gg, and hh ?

D

The table above gives selected values for a function ff. Based on the data in the table, which of the following could not be the graph of ff on the interval 1.9≤x≤2.11.9≤x≤2.1 ?

D

Let ff be the piecewise function defined above. Also shown is a portion of the graph of ff. What is the value of limx→2f(f(x))limx→2f(f(x)) ?

D. 1/2

The function ff is defined for all xx in the interval 4<x<64<x<6. Which of the following statements, if true, implies that limx→5f(x)=17limx→5f(x)=17 ?

D. There exist functions gg and hh with g(x)≤f(x)≤h(x)g(x)≤f(x)≤h(x) for 4<x<64<x<6, and limx→5g(x)=limx→5h(x)=17limx→5g(x)=limx→5h(x)=17.

If limx→6f(x)lim⁡x→6f(x) exists with limx→6f(x)<5limx→6f(x)<5 and f(6)=10f(6)=10, which of the following statements must be false?

D. ff is continuous at x=6x=6.

If ff is the function defined above, then limx→0f(x)limx→0f(x) is

D. nonexistent