1. 1 Section 1.2 Linear Functions Prepared by E. Gretchen Gascon

2. 2 Function Notation Function is an algebraic expression where for every x (the independent variable) there is one and only one y (the dependent variable) corresponding to it. A linear equation y = 4x – 3 can be written in function notation as y = f(x) = 4x - 3. x y f(x) You enter a value for x, and the function f(x) always outputs a unique value for y

3. 3 Problem # 13 page 27 Write a cost function given a set of parameters use c(x) to represent y instead of f(x) 10 items cost $650 to make. (the total cost) Given a fixed cost of $400 (the cost regardless of how many items are made, in other words the cost to produce 0 items c(0) = 400. Fixed Cost is the y- intercept (0,400) of a linear graph c(x) = mx + b OR c(x) = (unit cost) x + (fixed cost) Marginal (unit) cost is the slope (25/1) of the linear graph The unknown is the marginal cost. Substitute what you know into the cost function and solve for m. Rewrite the cost function using the value for m

4. 4 Graph of Problem #13 optional

5. 5 Problem # 19 page 29 graph the supply and demand functions on the same graph Supply equation Demand equation To graph in Excel: Create a table, let q be arbitrary, and solve for s(q) and d(q) Next, select the cells A1 : C13

6. 6 How to create the graph in Excel Choose the Chart wizard and select the xy(scatter) Screen may look slightly different in Excel 2007 Next: choose series in “columns”, you will see two lines that cross. You may then choose “Finish”

7. 7 Graph continued Select one of the dotted lines, and right click. From the menu select “Add Trendline” Repeat the process for the other line. Type: Linear Check: Display equation on chart The point of intersection is the equilibrium point. or Supply = Demand

8. 8 Problem #19 page 28 part b find the equilibrium quantity and the equilibrium price Set the supply function = the demand function and solve for q the equilibrium quantity. Multiply each side of the equation by the common denominator Next: substitute q into the supply function to find the equilibrium price. 36 strawberry-flavored licorice for $54

9. 9 Comments Was there anything about this PowerPoint presentation that you would like explained further? Post comments or questions to the Main Forum or your Individual Forum. For more examples be sure to review the Practice Exercises posted in the course materials Forum of our class.