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Represent relations Interpret graphs of relations

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Day 8. Represent relations Interpret graphs of relations. Relations. Using a coordinate graph system http://www.coolmath.com/algebra/08-lines/02-plotting-points-01.htm. Coordinate system Ordered pairs (x, y) Quadrants I, II, III, IV Y- coordinate X- coordinate X-axis Y-axis. - PowerPoint PPT Presentation
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Represent relations Interpret graphs of relations Relatio ns Day 8
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Page 1: Represent relations  Interpret graphs of relations

• Represent relations • Interpret graphs of relations

RelationsDay 8

Page 2: Represent relations  Interpret graphs of relations

Using a coordinate graph systemhttp://www.coolmath.com/algebra/08-lines/02-plotting-points-01.htm

Coordinate system

Ordered pairs (x, y)

Quadrants I, II, III, IV

Y- coordinate

X- coordinate

X-axis

Y-axis

Page 3: Represent relations  Interpret graphs of relations

Representation of a Relation

• Domain and Range• Ordered Pairs: (1,2), (-2, 4), (0, -3) • Table Graph Map

x y

Page 4: Represent relations  Interpret graphs of relations

Representation of a Relation

• Domain and Range• Ordered Pairs: (2,5), (-2, 3), (5, -2), (-1, -2) • Table Graph Map

x y

Page 5: Represent relations  Interpret graphs of relations

What are three ways to represent a relation?

***Show {(4, -3), (3,2, (-4,1), (0, -3)} as a relation in three ways.

Page 6: Represent relations  Interpret graphs of relations

Independent and Dependent variables

• Identify the independent and dependent variables:

• The committee is selling tickets to the Fall Ball. The tickets that they sell, the greater the amount of money they can spend for decorations.

• Independent: Dependent:

• Generally, the average price of going to the movies has steadily increased over time.• Independent: Dependent:• The air pressure inside a tire increases with the temperature.• Independent: Dependent:• As the amount of rain decreases, so does the water level of the river.• Independent: Dependent:

Page 7: Represent relations  Interpret graphs of relations

Interpreting graphs

• http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut9_bar.htm

Page 8: Represent relations  Interpret graphs of relations

Functions• Determine whether a relation is

a function• Find function values

Page 9: Represent relations  Interpret graphs of relations

What is a function?• A function is a relationship between input and out put. In a function there is

exactly one output for each input.• A function is a relation in which each element of the domain is paired with

exactly one element of the range• Domain Range

-3034

5321

Page 10: Represent relations  Interpret graphs of relations

What is a function?• A function is a relationship between input and out put. In a function there is

exactly one output for each input.• A function is a relation in which each element of the domain is paired with

exactly one element of the range• Domain Range

-2034

-369

Domain 1 3 4 1

Range 4 2 4 -4

Is this a function – why or why not?

Page 11: Represent relations  Interpret graphs of relations

At an ice sculpting competition, each sculpture’s height was measured to make sure that it was within the regulated height range of 0 to 6 feet. The measurements were as

follows: Team 1, 4 feet;; Team 2, 4.5 feet; Team 3, 3.2 feet; Team 4, 5.1; Team 5, 4.8.• Make a table

Determine the domain and range of the function Write the data as a set of ordered pairs. Then graph the data data.

• State whether the function is discrete or continuous.

Page 12: Represent relations  Interpret graphs of relations

Equations as Functions

• -3x + y = 8• Y = 8 + 3y• You can check If it is a function Using the verticalLine testx y

Page 13: Represent relations  Interpret graphs of relations

Discrete vs. continuous

• Discrete Continuous

• Use the vertical line test to check if it is a function.

Page 14: Represent relations  Interpret graphs of relations

Function notation

• F(x) = -4x + 7 • F(2) F(-3) +1

Page 15: Represent relations  Interpret graphs of relations

h(t) = -16+ 68t +2

• h(4)

2[h(g)]

Page 16: Represent relations  Interpret graphs of relations

Assignment

• Chapter Test – Thursday• Pp 44-46; 9-20, 40, 42-60• Pp.51-54; 20-44, 49, 50,52,54-75

Page 17: Represent relations  Interpret graphs of relations
Page 18: Represent relations  Interpret graphs of relations

You identified functions and found function values.

Identify and interpret key features of the graphs of functions.

Page 19: Represent relations  Interpret graphs of relations

Linear v. Non-Linear

LinearGraph that is a straight line.

Non-LinearGraph that is not a straight line.

Page 20: Represent relations  Interpret graphs of relations

Intercepts: Graph touches an axis

X-interceptsThe x-coordinate of the point at which a graph intersects the x-axis.

Y-interceptsThe y-coordinate of the point at which a

graph intersects the y-axis.

Page 21: Represent relations  Interpret graphs of relations

Line of Symmetry

Each half of the graph on either side of the line matches exactly.

Page 22: Represent relations  Interpret graphs of relations

End Behavior

Page 23: Represent relations  Interpret graphs of relations

Extrema: Relatively high/low points

Relative MinimumRelative Maximum

Page 24: Represent relations  Interpret graphs of relations

Positive v. Negative

PositiveWhere the graph lies above the x-axis.

NegativeWhere the graph lies below the x-axis.

Page 25: Represent relations  Interpret graphs of relations

Increasing v. Decreasing

IncreasingWhere the graph goes up.

DecreasingWhere the graph goes down.

Page 26: Represent relations  Interpret graphs of relations

Describe/ label the following features of the function below:

• Linear or Non-Linear? non-linear• x-intercept and y-intercepts?

x=7.2 and y=30• Line of symmetry? none• Positive/ negative?

positive: 0 < t < 7.2negative: t > 7.2 minutes

• Increasing/ decreasing?increasing: t < 1, 4 < t < 6decreasing: 1 < t < 4, t > 6

• Extrema?min: t = 4max: t = 1 and t = 6

• End behavior? As x increases, y decreases. As x decreases, y decreases.

Page 27: Represent relations  Interpret graphs of relations

Describe/ label the following features of the function below:

• Linear or Non-Linear? • x-intercept and y-intercepts?

x=5.5 and y=80• Line of symmetry? • Positive/ negative?

Positive: between x = 0 and x = 5.5 Negative: for about x > 5.5

• Increasing/ decreasing?Increasing: between x = 1 and x = 4Decreasing:for x < 1 and x > 4

• Extrema?Maximum: at about x = 4Minimum: at about x = 1

• End behavior? As x increases, y decreases. As x decreases, y increases.

Non-linear

None

Page 28: Represent relations  Interpret graphs of relations
Page 29: Represent relations  Interpret graphs of relations

Activity

• Draw a graph using at least 3 of the features discussed today.

• In complete sentences on the back of the graph, explain how the three terms are demonstrated in the graph you drew.


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