Deck 2: Functions and Graphs

Question 1

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

-y = x + 3

A)
B)
C)
D)

Answer 1

Question 2

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

-

A)
B)
C)
D)

Answer 2

Question 3

Determine whether the graph is the graph of a function.

-

A) function
B) not a function

Answer 3

not a function

Question 4

Determine whether the graph is the graph of a function.

-

A) function
B) not a function

Question 5

Determine whether the graph is the graph of a function.

-

A) function
B) not a function

Question 6

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

-

A) function
Domain:{15, 20, 25, 30}
Range: { 3, 4, 5, 6}
B) function
Domain: { 3, 4, 5, 6}
Range: {15, 20, 25, 30}
C) not a function

Question 7

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 8

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

-{( 41, -2), ( 5, -1), ( 5, 0), ( 6, 1), ( 14, 3)}

A) function
Domain: { 41, 6, 5, 14}
Range: { -2, -1, 0, 1, 3}
B) function
Domain: { -2, -1, 0, 1, 3}
Range: { 41, 6, 5, 14}
C) not a function

Question 9

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

-{( -2, 2), ( -1, -1), (0, -2), ( 1, -1), ( 3, 7)}

A) function
Domain: { -2, -1, 0, 1, 3}
Range: { 2, -1, -2, 7}
B) function
Domain: { 2, -1, -2, 7}
Range: { -2, -1, 0, 1, 3}
C) not a function

Question 10

Determine whether the function is linear, constant, or neither:

-

A) Linear
B) Constant
C) Neither

Question 11

Determine whether the function is linear, constant, or neither:

-

A) Linear
B) Constant
C) Neither

Question 12

Determine whether the function is linear, constant, or neither:

-

A) Linear
B) Constant
C) Neither

Question 13

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

-

A)
B)
C)
D)

Question 14

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( 10).

A) 10
B) -20
C) 0
D) 15

Question 15

Find the function value:

-Find f( 4) when

A) 137
B) -119
C) -23
D) -55

Question 16

Find the function value:

-

A)
B)
C)
D)

Question 17

Find the function value:

-Given that , find f(t + 2).

A)
B)
C) 3t + 6
D)

Question 18

Question 19

Question 20

Question 21

Compute and simplify the difference quotient

-

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

Question 22

Determine the domain of the function:

-f(x) = - 7x + 9

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

Question 23

Determine the domain of the function:

-

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

Question 24

Determine the domain of the function:

-

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

Question 25

Determine the domain of the function:

-

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

Question 26

Only one of the following functions has domain which is not equal to all real numbers. State which function and state its domain.

A)
B)
C)

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:
-

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

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:
-y = x² - 8

A) A function with domain ℛ
B) Not a function; for example, when x = -8, then y = ±1

Question 29

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 = -5

A) A function with domain all real numbers except x = 0
B) Not a function; for example, when x = -5, y = ±1

Question 30

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 = 1

A) A function with domain all real numbers except x = -3
B) Not a function; for example, when x = 1, y = ±3

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:
-x² + y² = 36

A) A function with domain ℛ
B) Not a function; for example, when x = 0, y = ±6

Question 32

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) Not a function; for example, when x = 5, y = ±4

Question 33

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 long. Round your answer to the nearest four decimal places.

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

Question 34

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 long. Round your answer to the nearest four decimal places.

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

Question 35

The function P, given by P(d) = d + 1, 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) 200 atm
B) 7 atm
C) 201 atm
D) 8 atm

Question 36

Give the domain and range of the function.

-

A) Domain: [0, $\infty$ ); Range: [0, $\infty$ )
B) Domain: [ 2, $\infty$ ); Range: all real numbers
C) Domain: all real numbers; Range: [2, $\infty$ )
D) Domain: all real numbers; Range: [ 5, $\infty$ )

Question 37

Give the domain and range of the function.

-

A) Domain: all real numbers; Range: [-4, $\infty$ )
B) Domain: [0, ?); Range: [0, $\infty$ )
C) Domain: all real numbers; Range: [ 2, $\infty$ )
D) Domain: [ 4, $\infty$ ); Range: all real numbers

Question 38

Give the domain and range of the function.

-

A) Domain: all real numbers; Range: (- $\infty$ , 4]
B) Domain: (- $\infty$ , 0]; Range: all real numbers
C) Domain: all real numbers; Range: (- $\infty$ , 0]
D) Domain: [0, $\infty$ ); Range: [0, $\infty$ )

Question 39

Give the domain and range of the function.

-

A) Domain: ( , $\infty$ ); Range: (- $\infty$ , 0]
B) Domain: (- $\infty$ , 5) $\cup$ ( 5, $\infty$ ); Range: (- $\infty$ , 0) $\cup$ (0, $\infty$ )
C) Domain: all real numbers; Range: [0, $\infty$ )
D) Domain: (- $\infty$ , 5]; Range: [0, $\infty$ )

Question 40

Give the domain and range of the function.

-

A) Domain: all real numbers; Range: [ - 5, $\infty$ )
B) Domain: all real numbers; Range: all real numbers
C) Domain: [ - 5, $\infty$ ); Range: all real numbers
D) Domain: all real numbers; Range: [0, $\infty$ )

Question 41

How can the graph of f(x) = - be obtained from the graph of

A) Shift it horizontally 1 units to the right. Reflect it across the x-axis.
B) Shift it horizontally -1 units to the left. 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 42

How can the graph of f(x) = - 6 be obtained from the graph of y = ?

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

Question 43

Write an equation for a function that has a graph with the given transformations:

-The shape of y = is shifted 5 units to the left. Then the graph is shifted 7 units upward.

A)
B)
C)
D)

Question 44

Write an equation for a function that has a graph with the given transformations:

-The shape 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 45

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 46

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 47

Graph the function.

-

A)
B)
C)
D)

Question 48

Graph the function.

-f(x) =

A)
B)
C)
D)

Question 49

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 50

If f(x) = , what is the definition of g(x), the function whose graph is obtained by shifting f(x)'s graph right 5 units and down 1 unit?

Question 51

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 p(x) = 625 - 5 , where 50 $\le$ x $\le$ 500. (i) Describe how the graph of the function p can be obtained from the graph of one of the six basic functions: y = x, y = , y = , or y = . (ii) Sketch a graph of function p using part (i) as an aid.

A)
B)
C)
D)

Question 52

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 53

The average weight of a particular species of frog is given by w(x) = 98 , 0.1 $\le$ x $\le$ 0.3, 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: y = x, , y = , y = , or y = . (ii) Sketch a graph of function w using part (i) as an aid.

A)
B)
C)
D)

Question 54

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

-

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

Question 55

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

-

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

Question 56

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

-

A) (A) x-intercepts: - 7, -1; y-intercept: 7
(B) Vertex ( -4, -9)
(C) Minimum: -9
(D) y $\ge$ -9
B) (A) x-intercepts: 1, 7; y-intercept: 7
(B) Vertex ( -4, -9)
(C) Minimum: -9
(D) y $\ge$ -9
C) (A) x-intercepts: - 7, -1; y-intercept: 7
(B) Vertex ( -4, -9)
(C) Maximum: -9
(D) y $\le$ -9
D) (A) x-intercepts: - 7, -1; y-intercept: 7
(B) Vertex ( 4, -9)
(C) Minimum: -9
(D) y $\ge$ -9

Question 57

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

-

A) (A) x-intercepts: -4, 2; y-intercept: -8
(B) Vertex ( 1, -9)
(C) Minimum: -9
(D) y $\ge$ -9
B) (A) x-intercepts: - 2, 4; y-intercept: -8
(B) Vertex ( 1, -9)
(C) Maximum: -9
(D) y $\le$ -9
C) (A) x-intercepts: - 2, 4; y-intercept: -8
(B) Vertex ( 1, -9)
(C) Minimum: -9
(D) y $\ge$ -9
D) (A) x-intercepts: - 2, 4; y-intercept: -8
(B) Vertex ( -1, -9)
(C) Minimum: -9
(D) y $\ge$ -9

Question 58

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

-

A) (A) x-intercepts: - 5, -1; y-intercept: -5
(B) Vertex ( -3, 4)
(C) Minimum: 4
(D) y $\ge$ 4
B) (A) x-intercepts: - 5, -1; y-intercept: -5
(B) Vertex ( 3, -4)
(C) Maximum: 4
(D) y $\le$ 4
C) (A) x-intercepts: - 5, -1; y-intercept: -5
(B) Vertex ( -3, 4)
(C) Maximum: 4
(D) y $\le$ 4
D) (A) x-intercepts: 1, 5; y-intercept: -5
(B) Vertex ( -3, 4)
(C) Maximum: 4
(D) y $\le$ 4

Question 59

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

-

A) (A) x-intercepts: 1, 5; y-intercept: -5
(B) Vertex ( 3, 4)
(C) Minimum: 4
(D) y $\ge$ 4
B) (A) x-intercepts: -5, - 1; y-intercept: -5
(B) Vertex ( 3, 4)
(C) Maximum: 4
(D) y $\le$ 4
C) (A) x-intercepts: 1, 5; y-intercept: -5
(B) Vertex ( -3, -4)
(C) Maximum: 4
(D) y $\le$ 4
D) (A) x-intercepts: 1, 5; y-intercept: -5
(B) Vertex ( 3, 4)
(C) Maximum: 4
(D) y $\le$ 4

Question 60

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 61

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 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

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 64

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

-

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

Question 65

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

-

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

Question 66

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

-

A) (- $\infty$ , -3]
B) [3, $\infty$ )
C) (- $\infty$ , 2]
D) [ - 2, $\infty$ )

Question 67

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

-

A) [-3, $\infty$ )
B) (- $\infty$ , -3]
C) [5, $\infty$ )
D) (- $\infty$ , -5]

Question 68

Find the vertex and the maximum or minimum of the quadratic function by first writing f in standard form. State the range of f and find the intercepts of f .

Question 69

Graph and indicate the maximum or minimum value of f(x), whichever exists.

Question 70

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

-

A)
B)
C)
D)

Question 71

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

-

A)
B)
C)
D)

Question 72

Solve graphically to two decimal places using a graphing calculator:

-

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

Question 73

Solve graphically to two decimal places using a graphing calculator:

-

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

Question 74

Solve the equation graphically to four decimal places:

-

A) No solution
B) -0.4341
C) -0.4341, 3.2912
D) 3.2912

Question 75

Solve the equation graphically to four decimal places:

-

A) No solution
B) -2.6235, 7.6235
C) -2.6235
D) 7.6235

Question 76

Solve the equation graphically to four decimal places:

-

A) 2.5000, 4.7500
B) 2.5000
C) 4.7500
D) No solution

Question 77

For the following problem, (i) graph f and g in the same coordinate system; (ii) solve f(x) = g(x) algebraically to two decimal places; (iii) solve f(x) > g(x) using parts i and ii; (iv) solve f(x) < g(x) using parts i and ii.

-f(x) = -0.8x(x - 8), g(x) = 0.4x + 3.2; 0 ? x ? 10

A)
B)
C)
D)

Question 78

In economics, functions that involve revenue, cost and profit are used. Suppose R(x) and C(x) denote the total revenue and the total cost, respectively, of producing a new high-tech widget. The difference represents the total profit for producing x widgets. Given R(x) = 60x - 0.4 and find the equation for P(x).

A)
B)
C)
D)

Question 79

In economics, functions that involve revenue, cost and profit are used. Suppose R(x) and C(x) denote the total revenue and the total cost, respectively, of producing a new high-tech widget. The difference represents the total profit for producing x widgets. Given R(x) = 60x - 0.4 and find P(100).

A) 55687
B) 313
C) 2000
D) 1687

Question 80

A professional basketball player has a vertical leap of 37 inches. A formula relating an athlete's vertical leap V, in inches, to hang time T, in seconds, is V= . What is his hang time? Round to the nearest tenth.

A) 1 sec
B) 0.6 sec
C) 0.9 sec
D) 0.8 sec