Example 3: Determine whether a) (2,13) and b) (-1,-3) lie on the graph of y=10x-7 c) sketch the graph by finding x- and y-intercepts. Example3.2: Find the equation of the line passing through the point (3,-2) with x-intercept -4 Example 6: (Using slope as a rate of change) A kitchen appliance manufacturing company determines that the total cost in dollars of producing x units of a blender is C= 25x+ 3500 .Describe the practical significance of the y-intercept and slope of this line. Example 7: (Depreciation: decreased in value) A college purchased exercise equipment worth $12,000 for the new campus fitness center. The equipment has a useful life of 8 years. The salvage value at the end of 8 years is $ 2000. Write a linear equation that describes the book value of the equipment each year. (The book value is the difference between the original value and the total amount of depreciation accumulated to date} Example 7.1: A machine worth $ 10,000 new and having a scrap value of $1000 is to be depreciated linearly over an 18-year life. What will be the value of the machine after 9 years? 2 Example 7.2: A piece of equipment has a cost function C(x) = 50 x +1000 function is R(x) = 500x - and its revenue x 2 , where x is in thousands of items. What is the least number of items that must be sold in order to break even? Example 7.3: At a price of $3.10 per gallon, the weekly demand by consumers for gas is 42gallons. If the price rises to $3.25 per gallon, the weekly demand by consumers drops to 39 gallons, Find a formula for Q, the weekly quantity of gas demanded in terms of p, the price per gallon, assuming that the demand is linear. Example 7: (Predicting sales) The sales for Best Buy were approximately $ 35.9 billion in 2006 and $40.0 billion in 2007. Using only this information, write a linear equation that gives the sales (in billions of dollars) in terms of the year. Then predict the sales for 2010. Introduction to Functions: 4 ways to represent a function a) Verbally b) Numerically c) Graphically d) Algebraically Example 8: Determine whether the relation represents y as a function of x. a) the input value x is the number of representatives from a state, and the output Value y is the number of senators. b) Input,x 2 2 3 4 5 Output ,y 11 10 8 5 1 Example 9: Let g(x) = - x 2+ 4 x +1. Find each function value . a g ( 2 ) b g ( 1 ) 2 c) g (t) d) g(x+2) Example 9: (A Piecewise-Defined Function) Evaluate the function when x=-1, 0 and 1. F(x) = { x 2 +1,x <0 0