Deck 1: Functions and Limits

Question 1

Find the limit.

Answer 1

Question 2

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

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the limit ,if it exists.

A)
B)
C)
D) Does not exist

Answer 3

Question 4

Choose an equation from the following that expresses the fact that a function f is continuous at the number 6.

A)
B)
C)
D)
E)

Question 5

Use continuity to evaluate the limit.

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

Question 6

Find the limit ,if it exists.

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

Question 7

Find the limit .

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

Question 8

Find the limit .

A)
B)
C) -1
D) 1

Question 9

Find the limit.

A)
B) 6
C) 5
D)
E) -6

Question 10

Let Find the following limits.

A) 3 and -3
B) both 3
C) both 1
D) 3 and -1
E) 3 and 1

Question 11

Find the limit.

A) 11
B) 5
C) 9
D) 18
E) 0

Question 12

Determine where f is discontinuous.

A) 0 only
B) 0 and -11
C) -11 only
D) 0 and 11
E) only

Question 13

Find the vertical asymptotes of the function.

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

Question 14

Determine where f is discontinuous.

Question 15

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

Question 16

If f and g are continuous functions with

A)
B)
C)
D)
E)

Question 17

Evaluate the limit.

A) -189
B) -1010
C) -1000
D) 135
E) -990

Question 18

Find the limit.

A)
B)
C)
D)
E)

Question 19

Evaluate the limit,if it exists.

A)
B) 1
C) -7
D)
E) does not exist

Question 20

For x = 5 determine whether f is continuous from the right,from the left,or neither.

Question 21

Evaluate the limit.

Question 22

The graphs of f(x) and g(x) are given.For what values of x is f(x) = g(x) ?

A) 4,2
B) 0
C) -2,5
D) -4,12
E)

Question 23

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

A)
B)
C)
D)
E)

Question 24

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

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

Question 25

Find an expression for the function y = f(x) whose graph is the bottom half of the parabola .

A)
B)
C)
D)
E)

Question 26

Evaluate the limit.

Question 27

The monthly cost of driving a car depends on the number of miles driven. Julia found that in October it cost her $200 to drive 300 mi and in July it cost her $350 to drive 600 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 28

If ,find and simplify ,where .

A)
B)
C)
D)

Question 29

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

Question 30

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) 54
B) 38
C) 30
D) 20
E) 35

Question 31

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 surface area of .
How many species of bats would expect to find in that cave?
(b)If you discover that 5 species of bats live in cave estimate the area of the cave.

Question 32

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

A)
B)
C)
D)

Question 33

If ,evaluate the difference quotient .

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

Question 34

Find the limit ,if it exists.

Question 35

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

Question 36

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

Question 37

A rectangle has perimeter 14 m.Express the area of the rectangle as a function of the length of one of its sides.

A)
B)
C)
D)
E)

Question 38

Find the limit .

Question 39

Find the domain of the function.

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

Question 40

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

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

Question 41

Which of the following graphs is neither even nor odd?

A)
B)
C)

Question 42

Find the domain of the function.

Question 43

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) f(x) = 1 and (ii) f(x) = 0.
c.Find the domain and range of f.

Question 44

Determine whether f is even,odd,or neither.

Question 45

If the point ( 7, 3 ) is on the graph of an even function,what other point must also be on the graph?

A) ( 7 , -3)
B) (0 , 0)
C) ( -7 , -3)
D) ( -7 , 3)
E) None of these

Question 46

Find the domain of the function.

Question 47

The graphs of f(x) and g(x) are given. Find the values of f (-4) and g (3).

Question 48

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

Question 49

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

A)
B)
C)
D)
E)

Question 50

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

A) Even
B) Neither
C) Odd

Question 51

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