GSE Math 7-8 Unit 7: FunctionsStudy Guide

Name ______

GSE8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Function or Not a Function?

/ This is a function. You can tell by tracing from each x to each y. There is only one y for each x; there is only one arrow coming from each x.
/ Ha! Bet I fooled some of you on this one! This is a function! There is only one arrow coming from each x; there is only one y for each x. It just so happens that it's always the same y for each x, but it is only that one y. So this is a function; it's just an extremely boring function!
/ This one is not a function: there are two arrows coming from the number 1; the number 1 is associated with two different range elements. So this is a relation, but it is not a function.
/ Okay, this one's a trick question. Each element of the domain that has a pair in the range is nicely well-behaved. But what about that 16? It is in the domain, but it has no range element that corresponds to it! This won't work! So then this is not a function. It isn’t even a relation!

Source: PurpleMath.com

Allfunctions are relations but not all relations are functions!

  1. In which relation is the domain equal to the range?
  2. {(-1,1),(-2,2),(-3,3),(-4,4)}
  3. {(1, -1),(2,-2),(3,-3),(4,-4)}
  4. {(1,1),(2,2),(3,3),(4,4)}
  5. {(-1,1),(-2,2),(-3,-3),(-4,-4)}
  1. Which of the following relations is a function?
  2. {(-2,0),(-1,0),(0,1),(1,0)}
  3. {(-3,-2),(-2,-2),(-2,-3),(-3,-3)}
  4. {(-1,-1),(-1,0),(-1,1),(0,-2)}
  5. {(0,-2),(-1,1),(1,-1),(0,1)}
  1. Which of the following describes the correspondence below?

a. Domainb. Relationc. Functiond. Range

Given the graph of a relation, if you can draw a vertical line that crosses the graph in more than one place, then the relation is NOT a function.

  1. Is the relation in the table a function? Explain why or why not in the space below.

x / y
0 / –5
1 / –1
1 / 3
1 / 6

5. This relation is NOT a function: {(0,5), (-6,6),(1,7),(7,1),(0,-1)}. Which of the ordered pairs must be omitted to make the resulting relation a function?

  1. (0,5)b. (-6,6)c. (1,7)d. (7,1)

6. Which relation is NOT a function?

  1. b.c.d.

GSE8.F.2Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greaterrate of change.

Algebraic Representation (Equation) / Table / Ordered Pair / Mapping / Graph
y = 4x – 3 / / (-2, -11)
(-1, -7)
(0, -3)
(1, 1)
(2, 5) / /

7. Write or draw an example of each for the input-output table below.

x / 1 / 2 / 3 / 4
y / 2 / 6 / 10 / 14

Ordered PairsGraphMappingEquation

8. Which of the graphs below is the graph of a function?

a. b. c. d.

  1. In a linear function, a constant change in x means a constant change in y.

Is the set of ordered pairs a linear function?

Explain why or why not.

  1. What missing value in the table below could make the function linear?

x / 2 / 3 / 4 / 5
y / 7 / ? / 17 / 22
  1. 10 b. 12c. 14d. 15
  1. Translate the equation y = 3x – 1 as a table, set of ordered pairs, and graph.
  2. What is the equation of the relation in the table below?

x / 0 / 1 / 2 / 3 / 4
y / 2 / 6 / 10 / 14 / 18

Ay =

By = 3x

Cy = x + 2

Dy = 4x + 2

  1. Which equation describes this function?

x / y
-3 / -27
-1 / -9
0 / 0
1 / 9
3 / 27
  1. y = 9xb. y = 3xc y = x + 9d. y = x – 8

For 14 - 15, find the rules for the following:

14. / 15.
y = / y =

16. A lift on a ski slope rises according to the equation a = 130t + 6250, where a is the altitude in feet and t is the number of minutes that a skier has been on the lift. Five friends are on the lift. What is the altitude of each person if they have been on the ski lift for the times listed in the table? Draw a graph that represents the relationship between the time on the lift and the altitude.

Skier / Time on Lift
Anna / 4 minutes
Tracy / 3minutes
Kwani / 2 minutes
George / 1.5 minutes
Tony / 1 minute

17. In an amusement park ride, a car travels according to the equation D = 1250t where t is time in minutes and D is the distance in feet the car travels. Below is a chart of the time that three people have been in the cars. Graph the relationship between time and distance. How far has each person traveled?

Rider / Time
Ryan / 1 minute
Greg / 2 minutes
Colette / 3 minutes

18. Write an equation that is NOT a LINEAR function. ______

19. Three friends are in a running club. The tables below are the representations of their data. Look over the tables and answer the following questions:

Are any of the relationships linear? Explain your answer.

Are any of them functions? Explain your answer.

Joe’s Running Rate (Friend #1)

Time (seconds) / Distance (meters)
0 / 0
1 / 2
2 / 9
3 / 11
4 / 20
5 / 25

Beth’s Running Rate (Friend #2)

Time (seconds) / Distance (meters)
0 / 0
2 / 3
4 / 6
6 / 9
8 / 12
10 / 15

Billie’s Running Rate (Friend #3)

D= 2.25 t
D represents distance
t represents time