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Chapter 4 Section 1: Linear Functions and Their Properties

Chapter 4 Section 1: Linear Functions and Their Properties. In this section, we will… Graph linear functions Identify the average rate of change of a linear function Determine whether a linear function is increasing, decreasing or constant over its domain

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Chapter 4 Section 1: Linear Functions and Their Properties

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  1. Chapter 4 Section 1: Linear Functions and Their Properties • In this section, we will… • Graph linear functions • Identify the average rate of change of a linear function • Determine whether a linear function is increasing, decreasing or constant over its domain • Solve applications of linear functions

  2. A linear function is a function of the form: It will have a slope of m and a y-intercept of (0, b) The slope(rate of change) of a line gives the line’s steepness. The average rate of change of a linear function is its slope. Why? 4.1 Linear Functions and Their Properties

  3. A linear function is …increasing over its domain if the slope is positive. …decreasing over its domain if the slope is negative. …constant over its domain if the slope is 0. What if the slope is undefined? 4.1 Linear Functions and Their Properties

  4. Example:Indicate the slope and coordinate of the y-intercept of the given linear function, then graph the function. • slope: • y-intercept: • Determine the average rate of change of the function. • Determine whether the function is increasing, decreasing or constant. 4.1 Linear Functions and Their Properties

  5. Example:Indicate the slope and coordinate of the y-intercept of the given linear function, then graph the function. • slope: • y-intercept: • Determine the average rate of change of the function. • Determine whether the function is increasing, decreasing or constant. 4.1 Linear Functions and Their Properties

  6. How to Solve a Word Problem: • Step 1: Read the problem until you understand it. • What are we asked to find? • What information is given? • What vocabulary is being used? • Step 2: Assign a variable to represent what you are looking for. • Express any remaining unknown quantities in terms of this variable. • Step 3: Make a list of all known facts and form an equation or inequality to solve. • It may help to make a labeled: diagram, table or chart, graph • Step 4: Solve • Step 5: State the solution in a complete sentence by mirroring the original question. • Be sure to include units when necessary. • Step 6: Check your result(s) in the words of the problem • Does your solution make sense? 4.1 Linear Functions and Their Properties

  7. Example:The monthly cost C, in dollars, for international calls on Quahog Cellular Company is given by the function where x is the number of minutes used. • What is the cost if you talk on • the phone for 50 minutes? • Suppose that your monthly bill is $29.32. How many minutes did you use? • Suppose that you budgeted $60 for the month for the phone. • What is the maximum number of minutes you can talk. 4.1 Linear Functions and Their Properties

  8. The quantity suppliedof a good or service is the amount of product a company is willing to supply at a given price. The quantity demandedof a good or service is the amount of product consumers are willing to purchase at a given price. equilibrium price Equilibrium occurs when supply = demand equilibrium quantity 4.1 Linear Functions and Their Properties

  9. Example:The quantity supplied S and the quantity demanded D of hot dogs at Quahog stadium are given by the following functions: • Where p is the price of a hot dog. • Find the equilibrium price for hot dogs at the game. What is the • equilibrium quantity. • Determine the prices for which quantity demanded is less than quantity • supplied. • What will happen to the price of hot dogs if quantity demanded is greater • than quantity supplied? 4.1 Linear Functions and Their Properties

  10. Depreciation is the reduction in value of an asset over its useful life. The simplest and most commonly used depreciation method, straight-line depreciation is calculated by taking the purchase or acquisition price of an asset subtracted by the salvage value divided by the total productive years the asset can be reasonably expected to benefit the company (called "useful life" in accounting jargon). Example:Quahog Phone Company purchases a new company car for $28,000. If the company depreciates the vehicle using the straight-line method over 7 years, what will be the annual depreciation of the car? We will assume there is no scrap-value. 4.1 Linear Functions and Their Properties

  11. Example:Suppose that a company has just purchased a new computer system for $36,000. The company chooses to depreciate the computer using the straight-line method over three years. • Write the linear function that expresses the book-value V of the computer as a function of its age x. • Graph the linear function. • What is the book value of • the computer after 2 years. • When will the computer system have a book value of $18,000. 4.1 Linear Functions and Their Properties

  12. Independent Practice You learn math by doing math. The best way to learn math is to practice, practice, practice. The assigned homework examples provide you with an opportunity to practice. Be sure to complete every assigned problem (or more if you need additional practice). Check your answers to the odd-numbered problems in the back of the text to see whether you have correctly solved each problem; rework all problems that are incorrect. Read pages 278-283 Homework: pages 284-287 #15, 17, 19, 37, 39, 41, 47 4.1 Linear Functions and Their Properties

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