MULTIPLE REPRESENTATIONS OF LINEAR RELATIONSHIPS

Problem 1 :

At the North parking garage it costs $5 to bring your car into the garage plus $2 for every hour the car is parked

For the above situation, find the following.

i) Equation

ii)  Table

iii)  Graph

Solution :

i)  Let x be the number of hours parked.

Cost spend for rent = 5

Equation = 5 + 2x

ii) Table

iii)  Graph :

Problem 2 :

The price of a small pizza is $6 plus $0.75 per topping. Complete each representation for this scenario below.

The total cost of the pizza depends on  _________

Find the following.

i)  Write the equation that models this situation.

ii) If Coach Torrey paid $9.75 for a pizza how many toppings did he get ?

iii)  Draw the mapping diagram

iv)  Represent it as table.

Solution :

The total cost of the pizza depends on number of toppings they use.

i)  Let x be the number of toppings and y be the total cost.

y = 6 + 0.75x

ii) 

Total cost = 9.75

6 + 0.75x = 9.75

0.75x = 9.75 - 6

0.75x = 3.75

x = 3.75/0.75

x = 5

iii)  Draw the mapping diagram

iv)  Represent it as table.

Problem 3 :

Gillian received a $15 gift card to download music for her mp3 player. Each song costs $1.50.

i) The data is discrete or continuous 

ii)  Write the set of all possible x-values

iii) Write the set of all possible y-values.

iv)  Can Gillian purchase 14 songs why or why not ?

Solution :

Worth of gift = $15

Number of songs she can download = x

i) Discrete

ii) 

15 = 1.5x

x = 15/1.5

x = 10

Possible x-values = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

iii) Possible y-values = {0, 1.5, 3, 4.5, 6, 7.5, 9, 12, 13.5, 15}

iv)  When number of songs (x) = 14

= 1.5(14)

= 21 > 15 (the worth of gift)

So, he cannot purchase 14 songs.

Problem 4 :

Swine flu is attacking Porkopolis. The function below determines how many people have swine flu where t = time in days and S = the number of people in thousands.

S(t) = 9t - 4

a) Find S(4)

b) What does S(4) mean ?

c) Find t when S(t) = 23

d) What does S(t) = 23 mean ?

Solution :

a) Find S(4)

S(4) = 9(4) - 4

S(4) = 32

b) What does S(4) mean ?

At the end of 4 days, 3200 people were attacked by the flu.

c) Find t when S(t) = 23

23 = 9t - 4

9t = 23 + 4

9t = 27

t = 27/9

t = 3

d) What does S(t) = 23 mean ?

At the end of 3 days, 2300 were attacked by flu.

Problem 5 :

Find 

i)   f(0)        ii)  f(2)       iii)   Find x, if f(x) = 4

Solution :

i)   f(0) = 3

ii)  f(2) = -1

iii)  f(x) = 4

Drawing the vertical line at -2, the line is intersecting the curve at 4. So, the value of x is -2.

Problem 7 :

The total bill for each customer at the lemanade stand is a function of the number of glasses of lemonade purchased. This relationship can be represented by 

f(x) = {(1, $2.50) (2, $5.00) (3, $7.50) (4, $10.00)}

Complete each representation for this scenario below.

i)  The total bill depends on ______

ii)  Represent in table.

iii)  How much would it for 6 glasses ?

iv) Write the equation that models this situation.

Solution :

i)  The total bill depends on number of lemonade

ii)  Represent in table.

iii)  How much would it for 6 glasses ?

Creating equation, we get

Total cost = 2.50x (x represents number of glasses of lemonade)

When x = 6

Total cost = 2.50(6)

= $15

iv) Write the equation that models this situation.

Total cost = 2.50x