Unit6:RelationsandFunctionsStudentTrackingSheet

Math10Common

Name:_________________________ Block:____

What I can do for this unit: After

Practice

After

Review

How I

Did

6-1 I can identify the domain and range of functions, identify the

dependent and independent variable, and describe or sketch a

possible situation for a given graph.

6-2 I can identify functions, non-functions, and one-to-one functions,

and also interpret functions.

6-3 I can use function notation to solve problems and input various

values, including monomials and binomials, into functions.

6-4 I can graph linear equations in various forms as well as solve

word problems involving linear equations.

6-5 I can graph and solve problems involving direct and indirect

variation.

6-6 I can identify linear and non-linear functions and graph them.

Code Value Description

N Not Yet Meeting Expectations I just don’t get it.

MM Minimally Meeting Expectations Barely got it, I need some prompting to help

solve the question.

M Meeting Expectations Got it, I understand the concept without help or

prompting.

E Exceeding Expectations Wow, nailed it! I can use this concept to solve

problems I may have not seen in practice. I also

get little details that may not be directly related

to this target correct.

Unit6:RelationsandFunctionsDay1Math10Common

6-1: I can identify the domain and range of functions, identify the dependent and independent

variable, and describe or sketch a possible situation for a given graph.

Last unit we looked at the Cartesian Coordinate system. We

will continue to do so in this unit. Notice how the

coordinate plane is divided into four quadrants:

Quadrant I, II, III, and IV.

Quadrant � �

I Positive Positive

II Negative Positive

III Negative Negative

IV Positive Negative

Plot and label each set of ordered pairs and state which quadrant they lie in, or which axis.

Be sure to label each point.

1) ��7, �3) 2) �7, �2) 3) �0, 3)

4) �4, 3) 5) ��5, 8) 6) �6, 0)

Relations are simply sets of ordered pairs ��, �). They can be expressed as equations, graphs, or as sets of

numbers. The first component of each set (the � values) is known as the domain. The second component of

each set (the � values) is called the range.

For example, the relation: �3, �8), �2, �5), ��8, 7), �3, �3) has a domain of {�8, 2, 3} and a range of

{�8, �3, �5, 7}.

Consider another relation, � = 3� + 2. We can put any value of � we want into this relation (input) and get a

calculated value for � (output). The � is known as then independent variable because we can choose any value

we want for it, it doesn’t depend on anything. However, � is calculated based on �. Thus � is the dependent

variable.

For our relation � = 3� + 2, we can express some values for it in different ways. The values of � we choose are

arbitrary. I will choose, � = �3, 0, 2 but we could choose any values we want. Three ways are shown below to

express these ordered pairs that are generated by these 3 values of �.

1. Ordered Pairs: ��3, �8), �0, 2), �2, 8)

2. Table of values:

Input ��) Relation � = �� + � Output ��)

�3 � = 3��3) + 1 �8

0 � = 3�2) + 2 2

2 � = 3�2) + 2 8

3. Map Notation

4. Graphically

�3

0

2

�8

2

8

Domain

Range

Determine the domain and range of the following relations.

7) {�1, 7), �4, 0), ��3, 4), �2,4)} 8) {��12, 15), ��8, 3), �5, 1)}

9)

10) 11)

12)

13)

14) 15)

16) 17) 18)

19) 20) 21)

22) 23) 24)

Answer the following questions.

25) Tracy has enough speed to coast her bicycle up and down a steep hill without pedaling. Which graph best represents her speed as a function of time?

26) A plane does a loop the loop. Which graph best shows its speed as a function of time?

27) Quebec has warm summers and cold winters. Which graph best represents Quebec’s average temperature versus the month?

28) Sharon takes a ski lift up to ski down Whistler. She stops to rest three times. Which graph best represents her descent?

29) James rides his bike around the neighbourhood. The graph below shows the distance from home versus the time. How long did it take for him to return home?

30) Sam is driving to Alberta. The graph shows his car’s fuel volume varying with time while he drives. The graph consists of four line segments. With stops included, Sam averages 90 km/h during the trip. Determine the rate of fuel consumption in litres per 100km.

31) The graph below shows the depreciation of a computer over time. What is the value of a $3500 computer after 36 months?

Unit6:RelationsandFunctionsDay2Math10Common

6-2: I can identify functions, non-functions, and one-to-one functions, and also interpret functions.

Review: Determine the domain and range of the following relations.

1) {�−6, 3�, �−2, 5�, �4, 0�, �4,1�}

2)

3)

4)

5)

6)

A function is a special type of relation in which for each domain value ��� there is only one value for the

range ���. We can check to see if a relation is a function by using the vertical line test, where we ensure that any

vertical line on the coordinate plane intersects the graph of the equation only once.

State whether each relation is a function or not.

7) {�−6, 3�, �−5, 1�, �4, 3�, �4,1�} 8) {�−2, 7�, �−2, 5�, �4, 0�, �5,1�} 9)

10)

11)

12)

13) 14) 15)

There are a special group of functions known as one-to-one functions. For these functions, every one value in the

domain ��� is associated with one value in the range ���. This means that these special functions must pass the

horizontal line test as well as the vertical line test.

For the relations above, state whether they are a one-to-one function.

16� 17� 18� 19� 20� 21� 22� 23� 24�

Use the following function to answer the questions below:

� −5 −3 −1 0 2 4 6 8

� 12 8 4 2 −2 −6 −10 −14

25� Write this function using mapping notation.

26� Graph this function.

27� Write an equation for this function in slope-intercept form.

Use the mapping notation below to answer the questions.

28� Express this function using the table below.

�

�

29� Graph this function.

−3

0

2

4

−8

2

8

15

Domain

Range

30�

31� The profit for a high school dance is given by the formula 1 = 83 − 400., where 3 is the number of tickets sold.

a. Graph this function. Label your axis, include a scale!

b. What does the � −intersect represent? What does the � −intercept represent?

c. Why does it not make sense to include negative � −values on this graph?

Unit6:RelationsandFunctionsDay3Math10Common

6-3: I can use function notation to solve problems and input various values, including monomials

and binomials, into functions.

Review: State whether each relation is a function, if it is a one-to-one function, and its domain and range.

1) {�−2,6�, �0,7�, �2, 6�, �1, −5�}

2)

3)

4)

5)

6)

Functions can be written using function notation. Function notation is just a different way of expressing functions.

Using function notation, we replace the with ����. Any letter can be used instead of �.

Consider = 2� − 1. Using function notation we would write ���� = 2� − 1. The � denotes that it is a function

� and the ��� tells us that it is dependent upon the independent variable �. For our function ���� = 2� − 1, we can

input any value of � into the function (domain) and it will output the " " value (range). Thus ��−3� = 2�−3� −

1 = −7

Find ��−5�, ��0�, and ��3� for each function.

7) ���� = 8� + 4 8) ���� =�

�� − 2 9) ���� = 2�� − 3

10) ���� = 15 − �� 11) ���� = 2�� + 3� − 1 12) ���� = �� + 3�� − 4

Now consider the function ���� = 5� − 3. If I know that ���� = 7, I can find out what value of � yields this

result. ���� = 7 = 5� − 3 → 10 = 5� → � = 2.

Answer the following.

13) If ���� = 2� − 5 and

���� = 17, find �. 14) If ���� = �� + 4 and

���� = 13, find �. 15) If ℎ��� = −

�

�� + 4, find

ℎ�5�. If ℎ��� = −4, find

�.

16) The profit for a concert is given by the

function � = 25� − 500, where � is the

profit and � is the number of tickets. If the profit is $11625, find the number of tickets sold.

17) The formula for the volume of a sphere is

given by � =

�!"�. Write this formula using

function notation and determine the volume of a sphere with radius 6 cm.

We are not limited to inputting numbers into functions. We can input other variables or combinations of variables

and numbers.

For example, if ���� = 8�� − 3, ��#� = 8#� − 3 (we simply replace � with #). ��☺)= 8☺�

− 3

I used ☺ in the previous example to show that we can plug anything at all in for �. Looking at ��☺)= 8☺�

− 4,

imagine that we want to plug in � + 3 instead of ☺. The function would then look like: ��� + 3� = 8�� + 3�� − 4

We could then simplify this expression: ��� + 3� = 8��� + 6� + 9� − 4 = 8�� + 48� + 68 .

For the same function, ��2�� = 8�2��� − 3 = 8�4��� − 3 = 32�� − 3.

Find ��−1�, �����, ��� − 3�, and ��3� + 1� for each function. Simplify and collect like terms.

18) ���� = 5� − 7 19) ���� = 3�� − 4 20) ���� = �� − 1

21) ���� = 8 − 2�� 22) ���� = 10� + 3 23) ���� = �� + 3� − 1

24� Make a table of values and graph the following function: ���� = 2�� − 3� + 4

�

25� Make a table of values and graph the following function: ���� = �� − 3�� + 3� + 1

�

Unit6:RelationsandFunctionsDay4Math10Common

6-4: I can graph linear equations in various forms as well as solve word problems involving linear

equations.

Review: Answer the following.

1) If ���) =

�� − 4 and

���) = 3, find �.

2) If ���) = −�

�� + 2 and

���) = 4, find �.

3) If ���) = −

�� + 4, find

��5). If ���) = −4, find �.

Find ��2), ��� + 2), and ��3�) for each function. Simplify and collect like terms.

4) ���) = 5� − 1 5) ���) = � + 1 6) ���) = �� − 3)

A linear equation is any equation that can be written in the form �� + �� = �. We recall from earlier

units that �� + �� = � is a straight line that can be arranged into various forms, such as slope-intercept

form �� = �� + ), general form ��� + �� + � = 0), and slope-point form �� − �" = ��� − �"). Note

that the form �� + �� = � is closest to (but not the same as) the general form.

All linear equations are functions except a vertical line (because it doesn’t pass the vertical line test!)

To graph any linear equation, 1. find the � −intercept (set � = 0 and solve for �).

2. find the � −intercept (set � = 0 and solve for �).

3. Find any third point by picking an arbitrary value for �, then solve for �.

4. Draw a straight line through the three points. If the three points don’t line up, there is a mistake.

Make a table of values for the three points picked (remember two are intercepts) and graph the following

linear equations and state whether they are functions. Circle whether the variable is the dependent or

independent variable. State the domain and range of each relation.

7) 4� + 3� = 24

� �

Dependent/

Independent

Dependent/

Independent

8) 3� + 3� + 9 = 0

� �

Dependent/

Independent

Dependent/

Independent

9) � = 4

� �

Dependent/

Independent

Dependent/

Independent

Graph the following linear equations. Label each equation as slope-intercept, general, slope-point form,

or other.

10) 10. 5� + 2� − 10 = 0

11) 11. � =�

�� − 8

12) 12. � = −2� + 3

13) 13. "

� − 0.6� − 0.1 = 0

Determine whether each ordered pair is a solution to the given equation.

14) �1, 3) 2� − 3� = −6 15) �5, 0) � = −"

&� + 1 16) �6, 8) � − 3 =

"

�� + 4)

Answer the following.

17) A car’s value is given by the equation 7 =30 − 5� where 7 is the value in thousands of dollars, and � is the value of years. Use the graph below to estimate its worth after three years.

18) The temperature of a cooling drink is given by > = −2� + 80 where > is the temperature in degrees and � is the time in minutes. Graph the equation and estimate the temperature after 15 minutes.

19) Sally has dimes and quarters in her pocket totalling $1.50. Graph this equation and list two possible combinations of coins.

20) The mark a student gets on his test is given by B = −5C + 90 where B is the percent on the test, and C is the time spent per week watching TV in hours. How long can she watch TV each week and still pass?

Write a rule to describe each function.

21) {�−8, 0), �−4, 3), �4,9) 22) {�−9, 13), �−3, 3), �6, −12) 23) The straight line with an � −intercept of 8 and a � −intercept of 18.

Answer the following.

24) Find the profit �I) for a concert that must pay the band $800 and charges $6.50 per ticket �C).

25) An all you can eat sushi place charges the following prices based on age: 0-3 years – free, 4-6 years - $5.00, 7-12 years – $10.00, and 13-100 years $15.00. What is the domain and range of the function where the price N is expressed as a function of age P?

26) Guido the bodybuilder’s weight Q can be expressed as a function of time C in weeks according to the equation Q = 0.5C + 75. How many weeks will it be before he weighs 200 kg?

Unit6:RelationsandFunctionsDay5Math10Common

6-5: I can graph and solve problems involving direct and indirect variation.

Review: State which quadrant or axis each point lies in.

1) �6, −2) 2) �0, −5) 3) �−4, −10) 4) �6, 0) 5) �2, 9) 6) �−3, 7)

7) Sarah buys a car for $40,000. It depreciates at a rate of $5,000 per year.

a. Graph this function. Label your axis, include a scale!

b. What does the " −intersect represent? What does the # −intercept represent?

c. Why does it not make sense to include negative " or # −values on this graph?

Direct and indirect variation are special cases of linear equations. Direct variation occurs when a linear equation

has a # −intercept of zero �# = %") so that the line passes through the origin. Indirect variation occurs when the

linear equation does not pass through zero �# = %" + ') where ' is a non-zero value.

Determine the whether each equation represents direct versus indirect variation.

8) # = −)

*" +

+

) 9) 8" = # 10) # − 4 =

)

,�" − 4)

Recall that with direct variation, the line always intersects the origin (since # = %", if " = 0, # = 0). Thus we

always know the point �0,0) is on the graph. We then only need one other point on the graph in order to determine

the slope.

Consider the case where # varies directly as " and when # = 12, " = −8. We can find % =-./-0

1./10=

2)/3

/4/3=

2)

/4=

−,

). Thus # = −

,

)".

Complete each table of values below and write an equation for the line. Assume # varies directly as ".

11)

" #

1

2 −8

3

4

5

12)

" #

−4

−2 −1

0

2

4

13)

" #

−8

−4

6 −2

6

12

14)

" #

24

12

−6

−18

8 −24

15) Supposing that # varies directly as ", what happens to " when # is doubled? What happens when # is halved?

16) Is the formula for the diameter of a circle = = 2>? an example of direct or indirect variation? Why?

17) An estimation of the amount of blood in the human body is that it varies directly in proportion to the person’s body mass. An 80kg person has a blood volume of about 6 L. Write an equation to express the blood volume as a function of body mass, and determine the blood volume of an 88 kg man and a 40 kg child.

18) A train travelling at 30 km/h needs 500 m to come to a complete stop. If stopping distance varies directly as speed, write an equation to express the stopping distance as a function of speed. Use this equation to determine how fast a train taking 800 m to stop was travelling. How far would it take for a train travelling at 70 km to stop?

19) The mass of garbage produced by a city varies directly by population. A city of 200 000 produces 125 tons of garbage every day. What mass of garbage would Abbotsford produce daily, assuming a population of 120 000 people? How big would a city be that produces 175 tons of garbage daily?

20) For a fundraiser, Alex has pledges totalling $12.50 per km run. Write the equation relating the amount collected and the distance covered. How far will he need to run to raise $150?

Unit6:RelationsandFunctionsDay6Math10Common

6-6: I can identify linear and non-linear functions and graph them.

Review: Determine the domain and range of the following relations.

1) 2) 3)

Find ��−3), ��2� + 1), and ��2�) for each function. Simplify and collect like terms.

4) ���) = 3� − 4 5) ���) = � + 2� − 1 6) ���) = !

� − 5

Sketch a rough graph for each of the following scenarios.

7) The height of a baseball thrown in the air as a function of time.

8) Average temperature in Abbotsford starting in January.

9) The height above the ground of a passenger on a Ferris wheel.

Most of the functions we have looked at in previous lessons are linear functions – functions that form straight lines

when graphed. However, many functions are non-linear. Linear functions can always be arranged into the form

0� + 12 = 3 whereas non-linear functions cannot.

Identify each as a linear or non-linear function. If it is linear, arrange it in the form 0� + 12 = 3.

10) 32 − 8� = 15 11) 2 = 456

12) 22 = � + 4

13) 2 = − 78

� + 3 14) 152 = 74 15) 2 = �! + 3� − 5

These are often more work to graph. To graph these, we need to make a table of values to graph and plot them.

For example, we will graph 2 = �9:. We note that this is equivalent to 2 = ;√�: =

so we pick perfect cubes for our

� values. We then fill between the points as best we can. Note that sometimes we may need to change the scale. If

we do, be sure to label your scale.

� 2 −8 4 −1 1 0 0 1 1 8 4

16) Make a table of values and graph the following function: ���) = 64

�

2

17) Make a table of values and graph the following function: ���) = �:9

�

2

18) Make a table of values and graph the following function: ���) = √�

�

2

19) Make a table of values and graph the following function: ���) = √� − 1

�

2

Unit6:RelationsandFunctionsDay7Math10Common

Review

Determine the domain and range of the following relations.

1) {�5 7), �3, −7), �−3, 2), �−3,7)} 2) 3) = �� + 3

Sketch a function that describes each situation..

4) A child coasts her bike down a hill and up the other side �no pedalling). Graph the child’s speed versus time.

5) A football is kicked high in the air, then caught by the receiver. Sketch the height versus the time.

State whether each relation is a function or not.

6)

7) {�−5, 8), �−1, 6), �−1, 0), �3,5)}

8)

9) The temperature of a cup of coffee left outside in Saskatoon in January is given by the function 4 = 90 − 1.55, where 4 is the temperature in degrees Celsius and 5 is the time in minutes.

a. Graph this function. Label your axis, include a scale. Be sure to choose a scale so that you include

the � and −intercept.

b. What does the � −intersect represent? What does the −intercept represent?

c. Why does it not make sense to include negative � −values on this graph?

10) Make a table of values and graph the following function: 9��) = �� − 2� + 1

�

Find 9�4), 9�6�), and 9�� − 2) for each function. Simplify and collect like terms.

11) 9��) = 5� + 3 12) 9��) = �� − � + 3 13) 9��) =:

;� + 2

Identify each as a linear or non-linear function. If it is linear, arrange it in the form <� + = = >.

14) 5 + 7� = 12 15) 2 � = �: + 5� 16) =?

:@�A

17) = −B

:� − 2 18) − 3 =

C

?�� − 2) 19) 15 =

B

A

Graph the following linear equations. Label each equation as slope-intercept, general, slope-point form,

or other.

20) − 3 = −�

:�� + 1)

21) 6� + 3 − 6 = 0

22) Jack has nickels and dimes in his pocket totalling $0.80. Graph this equation and list three possible combinations of coins.

23) A lift pass costs $200 and the daily rental cost of skiis is $25 at the local mountian. Thus the total cost of skiing for the season for Susan is given by > = 25F + 200, where > the total cost and F is the number of day she skis. Graph the function. How many days can she ski if she spends $325?

24) Make a table of values and graph the following function: 9��) =AI

;

�

25) Make a table of values and graph the following function: 9��) = −√�

�

Unit6:RelationsandFunctionsKeyMath10Common

Day 1

1) III 2) IV 3) � −axis 4) I 5) II 6) � −axis

7) D: {−3, 1, 2, 4} R: {0, 4, 7} 8) D: {−12, −8, 5} R: {1, 3, 15} 9) D: All real #’s R: � ≥ 0

10) −4 ≤ � ≤ 4 −4 ≤ � ≤ 4 11) D: All real #’s, � ≤ −2 12) D: All real #’s, R: All real #’s

13) D: {−3, −1, 1, 2, 4} R: {0, 1, 3, 4, 5} 14) �: �−2, 1� �: [−4, 1) 15) � > 0, � > 2

16) �: �1, 4) �: �−2, 4) 17) � ≥ 1 � ≤ 2 18) �: [−3, −1) �: [−2, 1]

19) �: [−1, 4) �: �−2, 1� 20) �: [−3, 1� �: �−3, 4� 21) �: �−2, 0) �: �−4, 0)

22) �: �−1, 4� � = −1,2 23) � = −3,1 �: [−1,3� 24) �: [−4,0� �: �−4.0), � = 2

25) b 26) e 27) b 28) c 29) c 30) e 31) a

Day 2 1) D: {−6, −2, 4} R: {0, 1, 3, 5} 2) D: All real #’s R: � ≥ 0 3) D: All real #’s, R: All real #’s

4) � ≥ −1 � ≤ 4 5) −3 ≤ � < 0 −1 ≤ � < 2 6) −3 < � ≤ 2 − 3 ≤ � < 2 7) No 8) No 9) Yes

10) Yes 11) No 12) No 13) Yes 14) No 15) No 7) No 8) No 9) Yes 10) No 11) No 12) No

13) Yes 14) No 15) No 18) � = −2� + 2 19) � �−3, 0, 2, 4) ��−8, 15, 2, 8) 21) a 22 b) �-intersect represents

number of tickets to break even, � −intersect represents loss if no tickets sold

22 c) can’t sell a negative number of tickets

Day 3

1) Function but not 1-1 D: {−2, 0, 2, 1} R:−5, 6, 7} 2) Function but not 1 − 1 D: All real #’s, � ≥ −4

3) 1-1 Function � > 3 � > −1 4) ) Function but not 1 − 1 −1 ≤ � < 4 − 3 < � ≤ 4

5) 1-1 Function −3 < � ≤ 2 −1 ≤ � < 2 6) 1-1 Function −3 < � ≤ 2 −3 ≤ � < 2

7) %�−5) = −36, %�0) = 4, %�3) = 28 8) %�−5) = − &'( , %�0) = −2, %�3) = 0

9) %�−5) = 47, %�0) = −3, %�3) = 15 10) %�−5) = 140, %�0) = 15, %�3) = −12

11) %�−5) = 34, %�0) = −1, %�3) = 26 12) %�−5) = −54, %�0) = −4, %�3) = 50

13) 11 14) ± 3 15) *( , 12 16) 485 17) 288+ cm( 18) %�−1) = −12, %��*) = 5�* − 7,

%�� − 3) = 5� − 22, %�3� + 1) = 15� − 2 19) %�−1) = −1, %��*) = 3�- − 4, %�� − 3) = 3�* − 18� +23, %�3� + 1) = 27�* + 18� − 1 20) %�−1) = 0, %��*) = �- − 1, %�� − 3) = �* − 6� + 8 %�3� + 1) = 9�* + 6� 21) %�−1) = 6, %��*) = 8 − 2�-, %�� − 3) = −2�* + 12� − 10 %�3� + 1) = −18�* − 12� + 6 22) %�−1) = −7, %��*) = 10�* + 3, %�� − 3) = 10� − 27

%�3� + 1) = 30� + 13 23) %�−1) = −3, %��*) = �- + 3�* − 1, %�� − 3) = �* − 3� − 1

%�3� + 1) = 9�* + 15� + 3

Day 4

1) *&* 2) − (

* 3) *( , 12 4) %�2) = 9, %�� + 2) = 5� + 9, %�3�) = 15� − 1 5) %�2) = 5, %�� + 2) = �* + 4� +

5, %�3�) = 9�* + 1 6) %�2) = 1, %�� + 2) = �* − 2� + 1, %�3�) = 9�* − 18� + 9

10) General 11) slope-int 12) slope-int 13) Other 14) No 15) Yes 16) Yes 17) $15,000

18) 50° 19) 0 dimes & 6 quarters, 5 dimes & 4 quarters, 10 dimes & 2 quarters, 15 dimes & 0 quarters

20) 8 hours 21) � = (- � − 6 22) � = − /

( � − 2 23) � = − 0- � + 18

24) 1 = 6.52 + 800 25) D: 0-100 R:0, 5, 10, 15 26) 250 weeks

Day 5

1) IV 2) � −axis 3) III 4) � −axis 5) I 6) II 7b) x-int represents when car is worth $0, y-int represents value of car

when new. C) no negative time, car won’t be worth less than 0

8) ind 9) direct 10) ind 11) −4, −12, −16, −20 12) −2, 0, 1, 2 13) 24, 12, −18, −36

14) −8, −4, 2, 6 15) � is doubled, � is halved 16) direct, no � −int 17) 6.6 L, 3L 18) 48 km/h, 1167 m

19) 125.6 tons, 280,000 20) 12 km

Day 6 1) −2 < � ≤ 4, 0 < � ≤ 4 2) � ≥ −2, � ≥ 0 3) −3 ≤ � < 1, −2 < � < 1 4) %�−3) = −13,

%�2� + 1) = 6� − 1, %�23) = 63 − 4 5) %�−3) = 2, %�2� + 1) = 4�* + 8� + 2

%�23) = 43* + 43 − 1 6) %�−3) = −7, %�2� + 1) = -( � − &(

( , %�23) = -( 3 − 5

10) 8� − 3� = −15 11) non 12) non 13) 6� + 5� = 15 14) non 15) non

16) 4−5, − &/5 , 4−4, − &

-5 , �3, &() etc. 17) �0, 0), �1, 1), �4, 8), �9, 27) etc.

18) �0, 0), �1, 1), �4, 2), �9, 3), �16, 4), etc. 19) �1, 0), �2, 1), �5, 2), �10, 3), �17, 4), etc.

Day 7 Review 1) �: {−3, 3, 5} �: {−7, 2, 7} 2) � > −4, � < 2 3) �: All real #’s, � ≥ 3 6) Yes 7) No 8) No

9b) when it hits 0˚, initial temp. 10) �−3, 16), �−2, 9), �−1, 2), �0 1), �1, 0), �2, 1), �3, 4), �4, 9) 11) %�4) = 23, %�6�) = 30� + 3, %�� − 2) = 5� − 7 12) %�4) = 15, %�6�) = 36�* − 6� + 3,

%�� − 2) = �* − 5� + 9 13) %�4) = 5, %�6�) = 0* � + 2, %�� − 2) = (

- � + &*

14) 7� + 5� = 12 15) non 16) non 17) 5� + 3� = −6 18) 6� − 7� = −9 19) non

20) slope-point 21) general 22) �0, 8), �2, 7), �4, 6) etc. 23) 5 days

24) �−4, −16), �−2, −2), 4−1, − &-5 , �0, 0), 41, &

-5 , �2, 2), �4, 16), �8, 128)

25) �0, 0), �1, −1), �4, −2), �9, −3), �16, −4), �25, −5), �36, −6), �49, −7)