Deck 2: Limits and the Derivative

Question 1

Determine whether the graph is the graph of a function.

A) function
B) not a function

Answer 1

function

Question 2

Determine whether the graph is the graph of a function.

A) function
B) not a function

Answer 2

not a function

Question 3

Provide an appropriate response.

Answer 3

Question 4

Determine whether the graph is the graph of a function.

A) function
B) not a function

Question 5

Determine whether the function is linear, constant, or neither
y - 12 = 0

A) Linear
B) Constant
C) Neither

Question 6

Determine whether the function is linear, constant, or neither

A) Linear
B) Constant
C) Neither

Question 7

Determine whether the function is linear, constant, or neither

A) Linear
B) Constant
C) Neither

Question 8

Determine whether the relation represents a function. If it is a function, state the domain and range.

A) function domain:{20, 45, 70, 95} Range: {4, 9, 14, 19}
B) function domain: {4, 9, 14, 19} range: {20, 45, 70, 95}
C) not a function

Question 9

Use point-by-point plotting to sketch the graph of the equation.

A)
B)
C)
D)

Question 10

Determine whether the function is linear, constant, or neither

A) Linear
B) Constant
C) Neither

Question 11

Find the function value.
Find f(-9) when ) when f(x

A) 68
B) 572
C) 131
D) -562

Question 12

Find the function value.
Given that at

A)
B)
C)
D)

Question 13

Determine whether the relation represents a function. If it is a function, state the domain and range.
{(-3, 10), (-2, 5), (0, 1), (2, 5), (4, 17)}

A) function domain: {-3, -2, 0, 2, 4} Range: {10, 5, 1, 17}
B) function domain: {10, 5, 1, 17} range: {-3, -2, 0, 2, 4}
C) not a function

Question 14

Determine whether the relation represents a function. If it is a function, state the domain and range.

A) function domain: {carrots, peas, squash}
Range: {Bob, Ann, Dave}
B) function domain: {Bob, Ann, Dave}
Range: {carrots, peas, squash}
C) not a function

Question 15

Use point-by-point plotting to sketch the graph of the equation.

A)
B)
C)
D)

Question 16

Use point-by-point plotting to sketch the graph of the equation.

A)
B)
C)
D)

Question 17

Provide an appropriate response.
For f(t) = 3t + 2 and g(t) = 2 , fi fnd 4f(3) - g(-3) + g(0).

Question 18

Find the function value.

A) 4
B)
C)
D)

Question 19

Determine whether the relation represents a function. If it is a function, state the domain and range.
{(41, -3), (5, -2), (5, 0), (9, 2), (21, 4)}

A) function domain: {-3, -2, 0, 2, 4} Range: {41, 9, 5, 21}
B) function domain: {41, 9, 5, 21} range: {-3, -2, 0, 2, 4}
C) not a function

Question 20

The graph of a function f is given. Use the graph to answer the question.
Use the graph of f given below to find f(-5).

A) 0
B) 8
C) -5
D) 3

Question 21

Provide an appropriate response.
For f(t) = 3 - 5t, find

Question 22

Solve the problem.
The function F described by F(x) = 2.75x + 71.48 can be used to estimate the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a woman whose
Humerus is 30.93 cm long. Round your answer to the nearest four decimal places.

A) 156.5375 cm
B) 43.3000 cm
C) 105.1600 cm
D) 13.5775 cm

Question 23

Determine the domain of the function.
f(x) = - 7x + 9

A) No solution
B) All real numbers
C)
D)

Question 24

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x
to which there corresponds more than one value of y.

A) A function with domain R
B) Not a function; for example, when x = 0, y = ±7

Question 25

Solve the problem.
The function P, given by ion P, given by gives the pressure, in atmospheres (atm), at a depth d, in feet, under the sea. Find the pressure at 200 feet. Round your answer to the nearest whole number.

A) 201 atm
B) 8 atm
C) 7 atm
D) 200 atm

Question 26

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x
to which there corresponds more than one value of y.
y = x

A)
B)

Question 27

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x
to which there corresponds more than one value of y.
xy + 3y = 5

A) A function with domain all real numbers except x = -3
B)

Question 28

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x
to which there corresponds more than one value of y.

A) A function with domain all real numbers except x = 5
B)

Question 29

Solve the problem.
To estimate the ideal minimum weight of a woman in pounds multiply her height in inches by 4 and subtract 130. Let W = the ideal minimum weight and h = height. W is a linear function of h. Find the ideal minimum
Weight of a woman whose height is 62 inches.

A) 378 lb
B) 130 lb
C) 118 lb
D) 120 lb

Question 30

Solve the problem.
The function M described by M(x) = 2.89x + 70.64 can be used to estimate the height, in centimeters, of a male whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a male whose
Humerus is 30.93 cm long. Round your answer to the nearest four decimal places.

A) 157.3400 m
B) 30.9300 cm
C) 160.0277 cm
D) 156.5375 cm

Question 31

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x
to which there corresponds more than one value of y.
xy = -7

A) A function with domain all real numbers except x = 0
B) Not a function; for example, when x = -7, y = ±1

Question 32

Compute and simplify the difference quotient quotient
f(x) = 5

A) 10x + 5h + 7
B) 15x - 7h + 14
C) 10x + 7
D)

Question 33

Determine the domain of the function.
f(x) =

A) All real numbers
B) x < 2
C) All real numbers except 2
D) No solution

Question 34

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x
to which there corresponds more than one value of y.

A)
B) Not a function; for example, when x = 10, y = ±1

Question 35

Determine the domain of the function.

A) No solution
B) All real numbers
C) x < 0
D) All real numbers except 0

Question 36

Solve the problem.
To estimate the ideal minimum weight of a woman in pounds multiply her height in inches by 4 and subtract 130. Let W = the ideal minimum weight and h = height. Express W as a linear function of h.

A) W(h) = 4 (h + 130)
B) W(h) = 4h - 130
C) W(h) = 130
D) W(h) = 130h + 4

Question 37

Solve the problem.
The point at which a company's costs equals its revenue is the break-even. C represents cost, in dollars, of x units of a product. R represents the revenue, in dollars, for the sale of x units. Find the number of units that must be produced
And sold in order to break even.
C = 15x + 12,000
R = 18x - 6000

A) 800
B) 12,000
C) 545
D) 6000

Question 38

Provide an appropriate response.
Only one of the following functions has domain which is not equal to all real numbers. State which function and state its
domain.
(A) h(x) (B)

Question 39

Determine the domain of the function.

A) x < 3
B)
C) No solution
D) All real numbers except 3

Question 40

Provide an appropriate response.
In a profit-loss analysis, point where revenue equals cost.

A) profit-loss point
B) inflection point
C) turning point
D) break-even point

Question 41

Provide an appropriate response.
Let T be the set of teachers at a high school and let S be the set of students enrolled at that school. Determine which of
the following correspondences define a function. Explain.
(A) A student corresponds to the teacher if the student is enrolled in the teacher's class.
(B) A student corresponds to every teacher of the school.

Question 42

Graph the function.

A)
B)
C)
D)

Question 43

Graph the function.

A)
B)
C)
D)

Question 44

Write an equation for a function that has a graph with the given transformations.
The shape of is shifted 5 units to the left. Then the graph is shifted 7 units upward.

A)
B)
C)
D)

Question 45

Give the domain and range of the function.

A)
B) Rang: all real numbers
C)
D) Range:

Question 46

Provide an appropriate response.
How can the graph of ow can the graph of f(x) 6 be obtained from the graph of 6 be obtained from the graph of y

A) Shift it horizontally 1 units to the left. Reflect it across the x-axis. Shift it 6 units up.
B) Shift it horizontally 1 units to the right. Reflect it across the y-axis. Shift it 6 units down.
C) Shift it horizontally 1 units to the right. Reflect it across the y-axis. Shift it 6 units up.
D) Shift it horizontally 1 units to the right. Reflect it across the x-axis. Shift it 6 units up.

Question 47

Find the x-intercept(s) if they exist.

A) -1, -5
B) 1 , 5
C) 10, -5
D)

Question 48

Solve the problem.
A retail chain sells washing machines. The retail price p(x) (in dollars) and the weekly demand x for a particular model are related by the function . (i) Describe how the graph of the
Function p can be obtained from the graph of one of the six basic functions: y or y = x . (ii) Sketch a graph of function p using part (i) as an aid.

A)
B)
C)
D)

Question 49

Give the domain and range of the function.

A)
B)
C)
D) ); Rang: all real numbers

Question 50

Provide an appropriate response.
, what is the defnition of g(x), the function whose graph is obtained by shifting f(x)'s
graph right 5 units and down 1 unit?

Question 51

Give the domain and range of the function.
h(x) =

A) , 0, ]; Range: all real numbers
B) ) )
C) , -3]
D) , 0 ]

Question 52

Solve the problem.
The average weight of a particular species of frog is given where x is length (with legs stretched out) in meters and w(x) is weight in grams. (i) Describe how the graph of function w can be
Obtained from one of the six basic functions: . (ii) Sketch a graph of
Function w using part (i) as an aid.

A)
B)
C)
D)

Question 53

Give the domain and range of the function.

A)
B) Domain: all real numbers; Range: all real numbers
C) Range: all real numbers
D)

Question 54

Write an equation for a function that has a graph with the given transformations.
The shape of pe of y is vertically stretched by a factor of 10, and the resulting graph is reflected across the x-axis.

A)
B)
C)
D)

Question 55

Graph the function.
Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each additional ounce or fraction of an ounce. Let L(x) be the cost of mailing a letter weighing x ounces. Graph y = L(x). Use the
Interval (0, 4].

A)
B)
C)
D)

Question 56

Provide an appropriate response.
The following graph represents the result of applying a sequence of transformations to the graph of a basic
function. Identify the basic function and describe the transformation(s). Write the equation for the given graph.

Question 57

Provide an appropriate response.
The following graph represents the result of applying a sequence of transformations to the graph of a basic
function. Identify the basic function and describe the transformation(s). Write the equation for the given graph.

Question 58

Solve the problem.
The following table shows a recent state income tax schedule for married couples filing a joint return in State X. (i) Write a piecewise definition for the tax due T(x) on an income of x dollars. (ii) Graph T(x). (iii) Find the tax due on a taxable income of $50,000. Of $95,000.

A)
B)
C)
D)

Question 59

Give the domain and range of the function.
s(x) =

A) Rang: :
B) ; Rang: : (
C)
D)

Question 60

Provide an appropriate response.
How can the graph of be obtained from be obtained from the graph of

A) Shift it horizontally -1 units to the left. Reflect it across the x-axis.
B) Shift it horizontally 1 units to the right. Reflect it across the x-axis.
C) Shift it horizontally 1 units to the left. Reflect it across the y-axis.
D) Shift it horizontally 1 units to the left. Reflect it across the x-axis.

Question 61

Find the range of the given function. Express your answer in interval notation.

A)
B)
C)
D)

Question 62

Find the vertex form for the quadratic function. Then find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range

A)
B)
C)
D)

Question 63

Write an equation for the graph in the form k, where a is either 1 or -1 and h and k are integers.

A)
B)
C)
D)

Question 64

Solve graphically to two decimal places using a graphing calculator.

A) x < -0.53 or x > 3.66
B) -0.53 < x < 3.66
C) -3.66 < x < 0.53
D) x < -3.66 or x > 0.53

Question 65

For the given function, find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range

A)
B)
C)
D)

Question 66

Find the range of the given function. Express your answer in interval notation.

A)
B)
C)
D)

Question 67

For the given function, find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range

A)
B)
C)
D)

Question 68

Determine whether there is a maximum or minimum value for the given function, and find that value.

A) Minimum: 4
B) Minimum: 0
C) Maximum: -4
D) Maximum: 10

Question 69

Solve graphically to two decimal places using a graphing calculator.

A) -0.93 < x < 2.46
B) -2.46 < x < 0.93
C) x < -2.46 or x > 0.93
D) x < -0.93 or x > 2.46

Question 70

For the given function, find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range

A)
B)
C)
D)

Question 71

Find the vertex form for the quadratic function. Then find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range

A)
B)
C)
D)

Question 72

Provide an appropriate response.
Find the vertex and the maximum or minimum of the quadratic function on by fir by first writing f in
standard form. State the range of f and find the intercepts of f .

Question 73

Find the x-intercept(s) if they exist.

A) 0
B) 0, 7
C) 7
D) 21

Question 74

Determine whether there is a maximum or minimum value for the given function, and find that value.

A) Minimum: 0
B) Maximum: - 9
C) Minimum: 9
D) Minimum: -9

Question 75

Provide an appropriate response.
Graph f(x) = and indicate the maximum or minimum value of f(x), whichever exists.

Question 76

Find the vertex form for the quadratic function. Then find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range

A)
B)
C)
D)

Question 77

Find the vertex form for the quadratic function. Then find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range
f(x)

A)
B)
C)
D)

Question 78

Write an equation for the graph in the form k, where a is either 1 or -1 and h and k are integers.

A)
B)
C)
D)

Question 79

Solve the equation graphically to four decimal places.
Let , find f(x) = 3.

A) 0.7922
B) 4.2078
C) No solution
D) 0.7922, 4.2078

Question 80

For the given function, find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range

A)
B)
C)
D)