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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
RelationsDay 8
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
Representation of a Relation
• Domain and Range• Ordered Pairs: (1,2), (-2, 4), (0, -3) • Table Graph Map
x y
Representation of a Relation
• Domain and Range• Ordered Pairs: (2,5), (-2, 3), (5, -2), (-1, -2) • Table Graph Map
x y
What are three ways to represent a relation?
***Show {(4, -3), (3,2, (-4,1), (0, -3)} as a relation in three ways.
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:
Interpreting graphs
• http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut9_bar.htm
Functions• Determine whether a relation is
a function• Find function values
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
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?
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.
Equations as Functions
• -3x + y = 8• Y = 8 + 3y• You can check If it is a function Using the verticalLine testx y
Discrete vs. continuous
• Discrete Continuous
• Use the vertical line test to check if it is a function.
Function notation
• F(x) = -4x + 7 • F(2) F(-3) +1
h(t) = -16+ 68t +2
• h(4)
2[h(g)]
Assignment
• Chapter Test – Thursday• Pp 44-46; 9-20, 40, 42-60• Pp.51-54; 20-44, 49, 50,52,54-75
You identified functions and found function values.
Identify and interpret key features of the graphs of functions.
Linear v. Non-Linear
LinearGraph that is a straight line.
Non-LinearGraph that is not a straight line.
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.
Line of Symmetry
Each half of the graph on either side of the line matches exactly.
End Behavior
Extrema: Relatively high/low points
Relative MinimumRelative Maximum
Positive v. Negative
PositiveWhere the graph lies above the x-axis.
NegativeWhere the graph lies below the x-axis.
Increasing v. Decreasing
IncreasingWhere the graph goes up.
DecreasingWhere the graph goes down.
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.
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
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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