Day 8 Relations Represent relations Interpret graphs of relations

Using a coordinate graph system http://www. coolmath 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. The air pressure inside a tire increases with the temperature. As the amount of rain decreases, so does the water level of the river.

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

Determine whether a relation is a function Find function values 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 -3 3 4 5 3 2 1

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 -2 3 4 -3 6 9 Domain 1 3 4 Range 2 -4 Is this a function – why or why not?

State whether the function is discrete or continuous. 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 vertical Line test x 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 𝑡 2 + 68t +2 h(4) 2[h(g)]

Assignment Chapter Test – Thursday Pp 44-46; 9-20, 40, 42-60

Review

You identified functions and found function values. Identify and interpret key features of the graphs of functions.

Linear v. Non-Linear Linear Graph that is a straight line. Non-Linear Graph that is not a straight line.

Intercepts: Graph touches an axis X-intercepts The x-coordinate of the point at which a graph intersects the x-axis. Y-intercepts The y-coordinate of the point at which a graph intersects the y-axis.

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

End Behavior

Extrema: Relatively high/low points Relative Minimum Relative Maximum

Where the graph lies below the x-axis. Positive v. Negative Positive Where the graph lies above the x-axis. Negative Where the graph lies below the x-axis.

Increasing v. Decreasing Where the graph goes up. Decreasing Where 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 < 7.2 negative: t > 7.2 minutes Increasing/ decreasing? increasing: t < 1, 4 < t < 6 decreasing: 1 < t < 4, t > 6 Extrema? min: t = 4 max: 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: Non-linear 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 = 4 Decreasing:for x < 1 and x > 4 Extrema? Maximum: at about x = 4 Minimum: at about x = 1 End behavior? As x increases, y decreases. As x decreases, y increases. 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.