Comparing Linear and Nonlinear Functions 5.5. ACTIVITY: Finding Patterns for Similar Figures. How can you recognize when a pattern

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1 5.5 Comparing Linear and Nonlinear Functions in real life is linear or nonlinear? How can ou recognize when a pattern ACTIVITY: Finding Patterns for Similar Figures Work with a partner. Cop and complete each table for the sequence of similar rectangles. Graph the data in each table. Decide whether each pattern is linear or nonlinear. a. Perimeters of Similar Rectangles b. Areas of Similar Rectangles 5 5 COMMON CORE Functions In this lesson, ou will identif linear and nonlinear functions from tables or graphs. Learning Standards 8.F. F.LE.b P P A A Chapter 5 Linear Functions

2 ACTIVITY: Comparing Linear and Nonlinear Functions Math Practice Interpret Results How do the graphs help ou to answer the question? Does our answer make sense? Work with a partner. The table shows the height h (in feet) of a falling object at t seconds. Graph the data in the table. Decide whether the graph is linear or nonlinear. Compare the two falling objects. Which one has an increasing speed? a. Falling parachute jumper b. Falling bowling ball t t h h h Parachute Jumper h Bowling Ball Height (feet) 8 Height (feet) Time (seconds) t Time (seconds) t. IN YOUR OWN WORDS How can ou recognize when a pattern in real life is linear or nonlinear? Describe two real-life patterns: one that is linear and one that is nonlinear. Use patterns that are different from those described in Activities and. Use what ou learned about comparing linear and nonlinear functions to complete Eercises 6 on page. Section 5.5 Comparing Linear and Nonlinear Functions 7

3 5.5 Lesson Lesson Tutorials The graph of a linear function shows a constant rate of change. A nonlinear function does not have a constant rate of change. So, its graph is not a line. Ke Vocabular nonlinear function, p. 8 Identifing Functions from Tables Does the table represent a linear or nonlinear function? Eplain. a. + Stud Tip A constant rate of change describes a quantit that changes b equal amounts over equal intervals. + b As increases b, increases b different amounts. The rate of change is not constant. So, the function is nonlinear. As increases b, decreases b 8. The rate of change is constant. So, the function is linear. + Identifing Functions from Graphs Does the graph represent a linear or nonlinear function? Eplain. a. b. The graph is not a line. So, the function is nonlinear. Eercises Does the table or graph represent a linear or nonlinear function? Eplain.. 8 Chapter 5 The graph is a line. So, the function is linear Linear Functions.

4 Identif a Function from an Equation Which equation represents a nonlinear function? A =.7 B = π C = D = ( ) You can rewrite the equations =.7, = π, and = ( ) in slope-intercept form. So, the are linear functions. You cannot rewrite the equation = in slope-intercept form. So, it is a nonlinear function. The correct answer is C. Stud Tip In Eample, the initial value of each function is $. Real-Life Application Account A earns simple interest. Account B earns compound interest. The table shows the balances for 5 ears. Graph the data and compare the graphs. Year, t Account A Balance Account B Balance $ $ $ $ $ $ $ $. $ $6. 5 $5 $6.5 Balance (dollars) Savings Account Account B Year Account A t Both graphs show that the balances are positive and increasing. The balance of Account A has a constant rate of change of $. So, the function representing the balance of Account A is linear. The balance of Account B increases b different amounts each ear. Because the rate of change is not constant, the function representing the balance of Account B is nonlinear. Eercises Does the equation represent a linear or nonlinear function? Eplain.. = = 6. = Section 5.5 Comparing Linear and Nonlinear Functions 9

5 5.5 Eercises Help with Homework. VOCABULARY Describe how linear functions and nonlinear functions are different.. WHICH ONE DOESN T BELONG? Which equation does not belong with the other three? Eplain our reasoning. 5 = = = 5 = 5 9+(-6)= +(-)= +(-9)= 9+(-)= Graph the data in the table. Decide whether the function is linear or nonlinear Does the table or graph represent a linear or nonlinear function? Eplain VOLUME The table shows the volume V (in cubic feet) of a cube with a side length of feet. Does the table represent a linear or nonlinear function? Eplain. Side Length, Volume, V Chapter 5 Linear Functions

6 Does the equation represent a linear or nonlinear function? Eplain.. + = 7. + = + 5. = 8 5. LIGHT The frequenc (in terahertz) of a light wave is a function of its wavelength (in nanometers). Does the table represent a linear or nonlinear function? Eplain. Color Red Yellow Green Blue Violet Wavelength, Frequenc, MODELING The table shows the cost (in dollars) of pounds of sunflower seeds. Pounds, Cost,.8? 5.6 a. What is the missing -value that makes the table represent a linear function? b. Write a linear function that represents the cost of pounds of seeds. c. What is the initial value of the function? d. Does the function have a maimum value? Eplain our reasoning. 7. TREES Tree A grows at a rate of.5 feet per ear. The table shows the height h (in feet) of Tree B after ears. a. Does the table represent a linear or nonlinear function? Eplain. b. Which tree is growing at a faster rate? Eplain. Years, Height, h PRECISION The radius of the base of a clinder is feet. Is the volume of the clinder a linear or nonlinear function of the height of the clinder? Eplain. 9. The ordered pairs represent a function. (, ), (, ), (, ), (, 9), and (, 6) a. Graph the ordered pairs and describe the pattern. Is the function linear or nonlinear? b. Write an equation that represents the function. Find the square root(s). (Skills Review Handbook) ± 9. MULTIPLE CHOICE Which of the following equations has a slope of and passes through the point (, )? (Section.6) A = + 6 B = ( + ) C = + 7 D = ( ) Section 5.5 Comparing Linear and Nonlinear Functions