Deck 15: The Nature of Graphs and Functions
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Deck 15: The Nature of Graphs and Functions
1
Is the set a function?
Answer yes or no.

Answer yes or no.
no
2
Find the difference quotient,
for the function given below.





3
Let P(x) be the number of prime numbers less than x. Find P(14).
P(14) = __________
P(14) = __________
6
4
Find the difference quotient,
for the given function.
__________



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5
If
, find h(3.8).
A)
B) 
C) 
D) 
E) 

A)

B)

C)

D)

E)

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6
It is estimated that t years from now, the population of a certain suburban community will be
Thousand people. What will the population of the community be 7 years from now?
A)
B) 
C) 
D) 
E) 

Thousand people. What will the population of the community be 7 years from now?
A)

B)

C)

D)

E)

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7
If
, find h(3.5). Round to two decimal places.
__________


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8
Is the set a function?
A) function
B) not a function

A) function
B) not a function
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9
Use the vertical line test to determine whether the curve is a function.
A) not a function
B) function

A) not a function
B) function
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10
For the given verbal description, write a rule in the form of an equation.
For each number x in the domain, the corresponding range value y is found by multiplying by 2 and then subtracting 7.
A)
B) 
C) 
D) 
E) 
For each number x in the domain, the corresponding range value y is found by multiplying by 2 and then subtracting 7.
A)

B)

C)

D)

E)

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11
Find the difference quotient,
for the given function.
A)
B) 
C) 
D) 
E) 


A)

B)

C)

D)

E)

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12
It is estimated that t years from now, the population of a certain suburban community will be
thousand people. What will the population of the community be 5 years from now?
__________ people

thousand people. What will the population of the community be 5 years from now?

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13
For the given verbal description, write a rule in the form of an equation.
For each number x in the domain, the corresponding range value y is found by multiplying by 5 and then subtracting 4.
For each number x in the domain, the corresponding range value y is found by multiplying by 5 and then subtracting 4.
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14
Sketch the parabola that has a distance between the directrix and its focus to be 4 units.
A) 
B)
C)
D) 
A)

B)

C)

D)

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15
Let P(x) be the number of prime numbers less than x. Find P(18).
A)
B) 
C) 
D) 
E) 
A)

B)

C)

D)

E)

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16
Find the difference quotient,
for the function given below.
A)
B) 
C) 
D) 
E) 


A)

B)

C)

D)

E)

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17
Use the vertical line test to determine whether the curve is a function.
The curve is __________ (a function, not a function).

The curve is __________ (a function, not a function).
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18
Is the set of ordered pairs a function?
A) function
B) not a function

A) function
B) not a function
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19
If
, list conditions on the constants to assure that the graph of a line results.
A) A and C have same signs
B) A = 0 and C = 0
C) A > C
D) A and C have opposite signs
E) A = C

A) A and C have same signs
B) A = 0 and C = 0
C) A > C
D) A and C have opposite signs
E) A = C
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20
Is the set of ordered pairs a function?
Answer yes or no.

Answer yes or no.
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21
If
, match each condition on the constants to the appropriate graph of the curve.
a.
b.
and
c.
and
have opposite signs
d.
and
have same signs
an ellipse

a.





d.


an ellipse
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22
Identify the curve.
This curve is __________ (parabola, line, circle, hyperbola).

This curve is __________ (parabola, line, circle, hyperbola).
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23
Sketch the graph of the equation.
A)
B) 
C) 
D) 

A)

B)

C)

D)

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24
Sketch the curve.
A)
B)
C)
D)

A)

B)

C)

D)

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25
If
, match each condition on the constants to the appropriate graph of the curve.
a.
b.
and
c.
and
have opposite signs
d.
and
have same signs
a line

a.





d.


a line
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26
A parabolic archway has the dimensions shown in the figure. Find the equation of the parabolic portion.
ft,
ft,
ft,
ft






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27
Sketch the graph of the equation.
A) 
B)
C)
D)

A)

B)

C)

D)

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28
Identify the curve.
This curve is __________ (line, circle, parabola, hyperbola).

This curve is __________ (line, circle, parabola, hyperbola).
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29
Sketch the curve.
A)
B)
C)
D)

A)

B)

C)

D)

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30
Sketch the curve.
A)
B)
C)
D)

A)

B)

C)

D)

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31
If
, match each condition on the constants to the appropriate graph of the curve.
a.
b.
and
c.
and
have opposite signs
d.
and
have same signs
a circle

a.





d.


a circle
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32
Identify the curve.
A) line
B) hyperbola
C) circle
D) no graph
E) parabola

A) line
B) hyperbola
C) circle
D) no graph
E) parabola
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33
If
, match each condition on the constants to the appropriate graph of the curve.
a.
b.
and
c.
and
have opposite signs
d.
and
have same signs
a hyperbola

a.





d.


a hyperbola
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34
Identify the curve.
A) point
B) hyperbola
C) parabola
D) circle
E) line

A) point
B) hyperbola
C) parabola
D) circle
E) line
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35
Beams of light parallel to the axis of the parabolic mirror shown in the figure strike the mirror and are reflected. Find the distance from the vertex to the point where the beams concentrate.
A = 12 ft, b = 8 ft
A) The focus is 32 in. from the vertex on the axis of the parabola.
B) The focus is 16 in. from the vertex on the axis of the parabola.
C) The focus is 12 in. from the vertex on the axis of the parabola.
D) The focus is 8 in. from the vertex on the axis of the parabola.
A = 12 ft, b = 8 ft

A) The focus is 32 in. from the vertex on the axis of the parabola.
B) The focus is 16 in. from the vertex on the axis of the parabola.
C) The focus is 12 in. from the vertex on the axis of the parabola.
D) The focus is 8 in. from the vertex on the axis of the parabola.
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36
Sketch the hyperbola with distance between the foci 10 units and the difference of the distances 6 units.
A)
B)
C)
D)
A)

B)

C)

D)

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37
Sketch the graph of the equation.
A)
B)
C)
D)

A)

B)

C)

D)

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38
Beams of light parallel to the axis of the parabolic mirror shown in the figure strike the mirror and are reflected. Find the distance from the vertex to the point where the beams concentrate.
ft,
ft
The focus is __________ in. from the vertex on the axis of the parabola.



The focus is __________ in. from the vertex on the axis of the parabola.
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39
A parabolic archway has the dimensions shown in the figure. Find the equation of the parabolic portion.
ft,
ft,
ft,
ft
A)
B)
C)
D)





A)

B)

C)

D)

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40
Sketch the graph of the equation.
A)
B)
C)
D)

A)

B)

C)

D)

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41
State whether the statement is true or false.
The test point
satisfies the inequality
.
The test point


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42
State whether the statement is true or false.
The test point
satisfies the inequality
.
The test point


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43
State whether the statement is true or false.
The test point
satisfies the inequality
.
The test point


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44
Find three ordered pairs that satisfy the equation.
A) (0 , 8), (1, 12), (2, 13)
B) (0 ,8) , (1, 9), (2, 10)
C) (0, 8), (1, 9), (2, 13)
D) (0, 8), (1, 12), (2, 10)
E) (1, 8), (2, 9), (3, 10)

A) (0 , 8), (1, 12), (2, 13)
B) (0 ,8) , (1, 9), (2, 10)
C) (0, 8), (1, 9), (2, 13)
D) (0, 8), (1, 12), (2, 10)
E) (1, 8), (2, 9), (3, 10)
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45
Sketch the graph of the equation.
A) 
B) 
C) 
D) 

A)

B)

C)

D)

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46
Graph the first-degree inequality in two unknowns.
A)
B)
C)
D)

A)

B)

C)

D)

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47
Graph the first-degree inequality in two unknowns.
A)
B)
C)
D)

A)

B)

C)

D)

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48
Graph the first-degree inequality in two unknowns.
A)
B)
C)
D)

A)

B)

C)

D)

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49
Graph the first-degree inequality in two unknowns.
A)
B)
C)
D) 

A)

B)

C)

D)

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50
Sketch the graph of the equation.
A) 
B) 
C) 
D)

A)

B)

C)

D)

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51
State whether the statement is true or false.
The test point
satisfies the inequality
.
The test point


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52
A learning curve describes the rate at which a person learns certain specific tasks. If N is the number of words per minute typed by a student. So for an average student
Where n is the number of days of instruction. What does the graph of this formula look like?
A)
B)
C)
D)

Where n is the number of days of instruction. What does the graph of this formula look like?
A)

B)

C)

D)

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53
Sketch the graph of the equation.
A) 
B) 
C)
D) 

A)

B)

C)

D)

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54
State whether the statement is true or false.
The test point (02, 3) satisfies the inequality
.
The test point (02, 3) satisfies the inequality

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55
Graph the first-degree inequality in two unknowns.
A)
B)
C)
D)

A)

B)

C)

D)

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56
State whether the statement is true or false.
The test point (0, 0) satisfies the inequality
.
The test point (0, 0) satisfies the inequality


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57
State whether the statement is true or false.
The test point (0, 0) satisfies the inequality
.
The test point (0, 0) satisfies the inequality


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58
State whether the statement is true or false.
The test point (-8, 9) satisfies the inequality
.
The test point (-8, 9) satisfies the inequality

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59
The healing law for skin wounds states that
Where A is the number of square centimeters of unhealed skin after t days when the original area of the wound was A 0 . Graph the healing curve for a wound of 50 cm 2 .
A)
B) 
C) 
D) 

Where A is the number of square centimeters of unhealed skin after t days when the original area of the wound was A 0 . Graph the healing curve for a wound of 50 cm 2 .
A)

B)

C)

D)

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60
Graph the first-degree inequality in two unknowns.
A)
B)
C)
D)

A)

B)

C)

D)

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61
Find three ordered pairs that satisfy the equation.


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62
Graph the line.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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63
Graph the line.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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64
Graph the line passing through (1, 3) with slope m = 1.5.
A)
B)
C)
D)
A)

B)

C)

D)

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65
If a present value P is invested at the simple interest rate r for t years, then the future value after t years is given by the formula
. Suppose you invest $15,000 at 8% simple interest per year. Graph the amount you will have in t years. What is the slope of the graph?
A) m = 1,200
B) m = 108
C) m = 1,340
D) m = 1,070
E) m = 1,270

A) m = 1,200
B) m = 108
C) m = 1,340
D) m = 1,070
E) m = 1,270
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66
Graph the line passing through (-2, 2) with slope m = 1.
A)
B)
C)
D)
A)

B)

C)

D)

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67
Find three ordered pairs that satisfy the equation.
A) (0, 4), (1, 8), (2, 8)
B) (0, 4), (1, 8), (2, 6)
C) (0, 4), (1, 6), (2, 8)
D) (0, 4), (1, 6), (2, 6)
E) (0, 4), (1, 6), (2, 16)

A) (0, 4), (1, 8), (2, 8)
B) (0, 4), (1, 8), (2, 6)
C) (0, 4), (1, 6), (2, 8)
D) (0, 4), (1, 6), (2, 6)
E) (0, 4), (1, 6), (2, 16)
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68
A business purchasing an item for business purposes may use straight-line depreciation to obtain a tax deduction. The formula for the present value, P, after t years is given below, where C is the cost and s is the scrap value after L years. The number L is called the useful life of the item.
If a certain piece of equipment costs $4,100 and has a scrap value of $1,700 after 5 years, write an equation to represent the present value after t years.
A)
B)
C)
D)
E)

If a certain piece of equipment costs $4,100 and has a scrap value of $1,700 after 5 years, write an equation to represent the present value after t years.
A)

B)

C)

D)

E)

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69
A business purchasing an item for business purposes may use straight-line depreciation to obtain a tax deduction. The formula for the present value, P, after t years is given below, where C is the cost and s is the scrap value after L years. The number L is called the useful life of the item.
If a certain piece of equipment costs $10,100 and has a scrap value of $1,700 after 8 years, graph the amount you will have in t years. What is the slope of the graph?
__________

If a certain piece of equipment costs $10,100 and has a scrap value of $1,700 after 8 years, graph the amount you will have in t years. What is the slope of the graph?

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70
A business purchasing an item for business purposes may use straight-line depreciation to obtain a tax deduction. The formula for the present value, P, after t years is given below, where C is the cost and s is the scrap value after L years. The number L is called the useful life of the item.
If a certain piece of equipment costs $8,100 and has a scrap value of $2,100 after 10 years, write an equation to represent the present value after t years.

If a certain piece of equipment costs $8,100 and has a scrap value of $2,100 after 10 years, write an equation to represent the present value after t years.
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71
Graph the line.
A)
B)
C)
D) 

A)

B)

C)

D)

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72
Find three ordered pairs that satisfy the equation.


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73
Graph the line.
A)
B)
C)
D)

A)

B)

C)

D)

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74
A business purchasing an item for business purposes may use straight-line depreciation to obtain a tax deduction. The formula for the present value, P, after t years is given below, where C is the cost and s is the scrap value after L years. The number L is called the useful life of the item.
If a certain piece of equipment costs $6,100 and has a scrap value of $2,300 after 5 years, graph the amount you will have in t years. What is the slope of the graph?
A)
B)
C)
D)
E)

If a certain piece of equipment costs $6,100 and has a scrap value of $2,300 after 5 years, graph the amount you will have in t years. What is the slope of the graph?
A)

B)

C)

D)

E)

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