college algebra math 130 amy jones lewis. moving a sand pile a relation is a function if for each...
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College AlgebraMath 130
Amy Jones Lewis
Moving a Sand Pile A relation is a function if for each input there
is exactly one output. Determine whether the relation below is a
function. (2, 6), (3, 9), (4, 12), (5, 15), (6, 18) (3, 3), (4, 1), (4, 6), (5, 0), (7, 5) (1, 2), (2, 3), (3, 0), (4, 1), (5, 0)
The set of all input values of a function is the domain of the function, and the set of all output values is the range of the function.
Solving Equations
300 – 5f = 725
1 - .15t = 9
10 = 14 – 2t
Write a story to describe each graph.
How would you describe the eating patterns of the six people shown?
Kettle Korn Tell a Story Graphs
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Donny’s Dinner Dilemma
The graphs show data for three dinner plans. Make observations about
each of the graphs. Find a way to determine
the cost for any number of meals purchased on each dinner plate and explain your reasoning.
Which dinner plan is best?
Donny’s Dinner Dilemma
Begin by individually making observations about each of the graphs, and then share your observations with your small groups.
Working with your group, find a way for determining the cost for any number of dinners in each plan. (Write an equation.)
Decide which plan is best.
Donny’s Dinner Dilemma
If you only had $45 to spend on food for the week, which dinner plan should you buy?
Does it make sense to connect the points in the dinner plan graphs? Why or why not?
Donny’s Dinner Dilemma
Describe another situation besides dinner card plans that would generate a formula and a graph similar to the graph of Plan A or Plan B.
Describe another situation that would give you a formula and a graph similar to the Regular Price Plan.
Donny’s Dinner Dilemma
What is the actual cost per meal for each of the plans if you consider the “activation fee”?
Graph the actual cost per meal as a function of the number of meals for each of the dinner card plans. (You can do this either by hand or with a graphing calculator.)
Donny’s Dinner Dilemma
(Hint -- If you buy two meals in Plan A the cost is $8 per meal plus $4 for the dinner card, so the actual cost per meal is $10).
Discussing the graph
List all of the pertinent information that can be read from the graph.(i.e. intersection points, when one deal is better than another…)
How would you describe the graph?
Donny’s Dinner Dilemma
Graph of Cost Per Meal
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Number of meals
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Regular price cost per meal
Plan A cost per meal
Plan B cost per meal
Donny’s Dinner Dilemma
Five Different Representations of a Function
Language
TableContext
Graph Equation
Homework Continue working on Donny’s Dinner Dilemma
Next Class: Wednesday, October 6