Deck 1: Functions and Limits

Question 1

Find the limit.

Answer 1

Question 2

Determine where f is discontinuous.

Answer 2

Question 3

Find the limit .

A)
B)
C)
D)1

Answer 3

Question 4

Find the limit , if it exists.

A)5
B)3
C)Does not exist
D)2

Question 5

Find the limit .

A)6
B)12
C)-1
D)-12

Question 6

Evaluate the limit.

A)
B)
C)
D)
E)

Question 7

Evaluate the limit, if it exists.

A)
B)1
C)
D)
E)does not exist

Question 8

Let Find the following limits.

A) and
B) and
C)both 1
D) and
E)both

Question 9

Determine where f is discontinuous.

A) only
B)
C) only
D)
E)0 only

Question 10

For determine whether f is continuous from the right, from the left, or neither.

Question 11

For the function f whose graph is shown, state the following.

Question 12

Find the limit , if it exists.

A)
B)
C)Does not exist
D)

Question 13

Find the limit.

A)
B)
C)
D)
E)

Question 14

Use continuity to evaluate the limit.

A)
B)0
C)1
D)
E)

Question 15

For what value of the constant c is the function f continuous on

A)
B)
C)
D)
E)

Question 16

Find the limit.

A)
B)
C)
D)
E)

Question 17

If f and g are continuous functions with

A)
B)
C)
D)
E)

Question 18

Choose an equation from the following that expresses the fact that a function f is continuous at the number .

A)
B)
C)
D)
E)

Question 19

Find the limit.

A)
B)
C)
D)
E)

Question 20

Find the vertical asymptotes of the function.

A)
B)
C)
D)
E)None of these

Question 21

If , find and simplify , where .

A)
B)
C)
D)

Question 22

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function. Complete the table and find the slope.

Question 23

Estimate the value of the following limit by graphing the function . Round your answer correct to two decimal places.

A)
B)
C)
D)3.18
E)

Question 24

Find the limit .

Question 25

If , evaluate the difference quotient .

A)h
B)
C)
D)
E)none of these

Question 26

The graph shown gives the weight of a certain person as a function of age. Find the age at which the person started an exercise program.

A)35
B)38
C)20
D)54
E)

Question 27

Evaluate the function at the given numbers (correct to six decimal places). Use the results to guess the value of the limit

Question 28

Many physical quantities are connected by inverse square laws, that is, by power functions of the form .In particular, the illumination of an object by a light source is inversely proportional to the square of the distance from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move the distance to the lamp. How much brighter is the light?

A) times
B) times
C) times
D) times
E) times

Question 29

By graphing the function and zooming in toward the point where the graph crosses the y-axis, estimate the value of

Question 30

Find the limit , if it exists.

Question 31

The graphs of and are given. For what values of x is ?

A)4, 2
B)
C)0
D)
E)-4, 12

Question 32

Find the domain of the function.

A)(- $\infty$ , 0) $\cup$ (0, $\infty$ )
B)(- $\infty$ , 0)
C)
D)

Question 33

Evaluate the limit.

Question 34

Use the graph of the function to state the value of , if it exists.

A)
B)
C)
D)does not exist
E)

Question 35

The monthly cost of driving a car depends on the number of miles driven. Julia found that in October it cost her to drive mi and in July it cost her to drive mi. Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a suitable model.

A)
B)
C)
D)
E)

Question 36

The graph of the function is given. State the value of .

A)
B)
C)
D)
E)

Question 37

Use the graph of the function to state the value of if it exists.

A)
B)
C)
D)1
E)does not exist

Question 38

It makes sense that the larger the area of a region, the larger the number of species that inhabit the region. Many ecologists have modeled the species-area relation with a power function and, in particular, the number of species S of bats living in caves in central Mexico has been related to the surface area A measured in of the caves by the equation (a) The cave called mission impossible near puebla, mexico, has suface area of .How many species of bats would expect to find in that cave?
(b) If you discover that species of bats live in cave estimate the area of the cave.

Question 39

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function. What is the F-intercept and what does it represent?

A)0, Fahrenheit temperature corresponding to
B) , Fahrenheit temperature corresponding to
C) , Celsius temperature corresponding to
D)32, Celsius temperature corresponding to
E)32, Fahrenheit temperature corresponding to

Question 40

Evaluate the limit.

Question 41

Determine whether f is even, odd, or neither.

Question 42

If f (x) = find f (-4), f (0), and f (1).

Question 43

A rectangle has perimeter m. Express the area of the rectangle as a function of the length of one of its sides.

A)
B)
C)
D)
E)

Question 44

An open rectangular box with volume has a square base. Express the surface area of the box as a function of the length of a side of the base.

A)
B)
C)
D)
E)

Question 45

Find the domain of the function.

Question 46

Which of the following graphs is neither even nor odd?

A)
B)
C)

Question 47

The graphs of and are given.Find the values of and .

Question 48

Determine whether the function whose graph is given is even, odd, or neither.

A)Even
B)Neither
C)Odd

Question 49

Determine whether the function is even, odd, or neither.

Question 50

Find the domain of the function.

Question 51

Find the domain and sketch the graph of the function. What is its range? f (x) =

A)D: (- ,
); R: [0,
)

B)D: (- ,
); R: (-
, 0]
(3,
)

C)D: (- ,
); R: (-
, 3]

D)D: (- ,
); R: [-1,
)

Question 52

Find an expression for the function whose graph is the bottom half of the parabola .

A)
B)
C)
D)
E)

Question 53

Refer to the graph of the function f in the following figure.
a. Find f (1).
b. Find the value of x for which (i)
and (ii)
.
c. Find the domain and range of f.

Question 54

If the point is on the graph of an even function, what other point must also be on the graph?

A)
B)
C)
D)
E)None of these