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Exploring Linear Functions in Real-world Scenarios

Learn to model real-world situations using linear functions with practical examples and graphical representations. Explore slope calculations, zero points, intercepts, and function graphs to master fundamental concepts. Dive into step functions and cost analysis models with engaging exercises.

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Exploring Linear Functions in Real-world Scenarios

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  1. Lesson 1-4 Linear Functions and Models

  2. Objective:

  3. Objective: To model real-world situations by means of linear functions.

  4. Function:

  5. Function: A dependent relationship between quantities.

  6. Linear Function:

  7. Linear Function:

  8. A) What is the slope of the graph of f(x) = -2x + 4?B) What is the zero of the function?C) What are the intercepts of the function’s graph?D) Find .

  9. The senior class has paid $200 to rent a roller skating rink for a fund raising party. Tickets for the party are $5 each.A) Express the net income as a function of the number of tickets sold.B) Graph the function. Identify the point at which the class begins to make a profit.

  10. Let g be a linear function such that g(1) = 2 and g(5) = 4.A) Sketch the graph of g.B) Find an equation for g(x).C) Find g(-1).

  11. Suppose that it costs 50 cents for the first minute of a long distance telephone call and 20 cents for each additional minute or fraction thereof. Give a graphical model of the cost of a call lasting t minutes.

  12. Suppose that it costs 50 cents for the first minute of a long distance telephone call and 20 cents for each additional minute or fraction thereof. Give a graphical model of the cost of a call lasting t minutes. Lets analyze the information: time ‘t’ cost If 0 < t < 1 ?? If 1 < t < 2 ?? If 2 < t < 3 ?? If 3 < t < 4 ?? This type of problem actually models what is called a ‘step function’. Can you figure out why?

  13. Assignment:Pgs. 21-22C.E. 1-4 all,W.E. 1-6 all, 7-15 odd, 21

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