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Study Matrix

Functions and Graphing

Name: __________________________________________

1. Match each scenario with its appropriate graph. (1 mark each)

A) a soccer balls distance above the ground as the goalie kicks the ball.

B) the speed of a subway train as it arrives at a station.

C) the number of un-popped kernels as a popcorn maker heats up and pops the corn.

D) the number of people in a building as they enter the building, watch a sporting event

and then leave the building.

2. Below is a graph where Michaela runs a race. Describe what each line segment means.

AB _______________________________________________________________________________

BC _______________________________________________________________________________

CD _______________________________________________________________________________

3. Determine if each relation is a linear relation or non-linear relation.

|[pic]|[pic] |[pic]|[pic] |[pic] |[pic] |

|[pic]|[pic] |[pic]|[pic] |[pic] |[pic] |

a)

a) _____________________________

b) [pic]

b) _____________________________

c)

c) _____________________________

4. Determine if each relation is a function or not a function.

|[pic]|[pic] |[pic] |[pic] |[pic] |[pic] |

|[pic]|[pic] |[pic] |[pic] |[pic] |[pic] |

a)

a) _____________________________

|[pic]|[pic] |[pic] |[pic]|[pic] |[pic] |

|[pic]|[pic] |[pic] |[pic]|[pic] |[pic] |

b)

b) _____________________________

c)

c) _____________________________

d)

d) _____________________________

e)

e) _____________________________

f)

f) _____________________________

5. Determine the domain and range of the following relations. (Answer in words, set and interval notation)

a)

set notation D: _____________________________

set notation R: _____________________________

interval notation D: _____________________________

interval notation R: _____________________________

b)

set notation D: _____________________________

set notation R: _____________________________

interval notation D: _____________________________

interval notation R: _____________________________

6. Graph [pic] on the grid provided using the three points in the table of values.

7. Graph [pic] on the grid provided using the x-intercept as one point and the y-intercept

as the other point.

8. A water tank in Leask, Saskatchewan holds 12 000 L. The graph below shows the relationship

between the water remaining in the tank and the time once the tank begins to drain.

a) Identify the dependent and independent variables.

dependent: _____________________________

1 mark

independent: _____________________________

1 mark

b) What does the [pic]-intercept represent in this situation.

b)________________________________________________________________________

1 mark

c) Determine the rate of change then describe what it represents.

rate of change: _____________________________

1 mark

Description, rate of change: ________________________________________________________

1 mark

9. What is the cost of hiring a carpenter for 8 hours?

9) _____________________________

2 marks

10. The cost [pic], in dollars, or renting a hall for an upcoming event and is given by the formula

[pic], where [pic] is the number of people attending the event.

a) Calculate the cost of renting the hall if 117 people attend.

a) _____________________________

2 marks

b) How many people attended the dance if it cost $845.

b) _____________________________

2 marks

c) State the dependent and independent variables.

Dependent: _____________________________

1 mark

independent: _____________________________

1 mark

11. Aleah was asked by her friend to take over delivering catalogues for one day. Below is a graph

that represents the income earned for 1 day’s work.

a) Determine the coordinates of the [pic]-intercept.

a) _____________________________

2 marks

b) What does the [pic]-intercept represent.

b) _________________________________________________________________________

1 mark

c) Determine the rate of change then describe what it represents.

rate of change: _____________________________

1 mark

Description, rate of change: ________________________________________________________

1 mark

12. Camille bought 120 doughnuts for $60. Her profit was $48 once she sold 80 doughnuts.

Write an equation that represents Camille’s profit [pic], as a function of the number of

doughnuts sold, [pic].

12) _____________________________

2 marks

13. The function [pic] is used to convert temperatures in degrees Celsius ([pic])

to temperatures in degrees Fahrenheit ([pic]).

a) Determine [pic]

a) _____________________________

b) Calculate the value of [pic] if [pic]

b) _____________________________

14. The graph of [pic] below. Determine the following.

a) [pic] a) _____________________________

1 mark

b) [pic] b) _____________________________

1 mark

-----------------------

[pic]

Time

[pic]

Time

[pic]

Time

[pic]

Time

iv) _________

iii) _________

ii) _________

i) _________

Michaela’s Race

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

S

p

e

e

d

m/s

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

Time (s)

2 marks

2 marks

2 marks

1 mark

1 mark

[pic]

[pic]

1 mark

1 mark

[pic]

[pic]

1 mark

[pic]

[pic]

1 mark

[pic]

[pic]

[pic]

[pic]

1 mark

1 mark

1 mark

Domain: ______________________________________

______________________________________

Range: ________________________________________

________________________________________

1 mark

1 mark

1 mark

1 mark

1 mark

1 mark

Domain: ______________________________________

______________________________________

Range: ________________________________________

________________________________________

1 mark

1 mark

1 mark

1 mark

1 mark

1 mark

[pic]

C

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

3 marks

[pic]

C

[pic]

[pic]

[pic]

[pic]

[pic]

3 marks

[pic]

[pic]

[pic]

[pic]

[pic]

Volume (L)

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

Time (min)

Cost hiring a Carpenter vs. Time

[pic]

[pic]

[pic]

Cost ($)

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

Time (h)

Income

($)

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

Number of catalogues

2 marks

2 marks

[pic]

C

[pic]

[pic]

[pic]

[pic]

[pic]

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