Compare Properties of Functions Chapter 4.5 Compare Properties of Functions

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Example 1 53<59 So, the zebra is faster than the lion. A zebra’s main predator is a lion. Lions can run at a speed of 53 feet per second over short distances. The graph shows the speed of a zebra. Compare their speeds. 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒 = 118−59 2−1 53<59 = 59 1 So, the zebra is faster than the lion.

A certain car has a gas mileage of 22 miles per gallon A certain car has a gas mileage of 22 miles per gallon. The gas mileage of a certain sport utility vehicle is represented by the function shown. Compare their gas mileage. 𝑚𝑖𝑙𝑒𝑠 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 = 38−19 2−1 = 19 1 22>19 So, the car gets better gas mileage than the sport utility vehicle.

Example 2 The function 𝑚=140ℎ, where 𝑚 is the miles traveled in ℎ hours, represents the distance traveled of the first Japanese high speed train. The distance traveled of a high speed train operating today in China is shown in the table. Assume the relationship between the two quantities is linear.

Example 2a Japanese Train 𝑚=140ℎ Compare the functions y-intercepts and constant rates of change. Both equations have a y-intercept of 0 because at 0 hours the trains have traveled 0 miles. 140<217 The Chinese Train has a greater rate of change. Chinese Train + 1 + 217 + 1 + 217 = 217 1

Example 2b If you ride each train for 5 hours, how far will you travel on each? Japanese Chinese 𝑚=140ℎ 𝑚=140 5 𝑚=700 700 miles 217 miles per hour 217(5) 1,085 miles

Example 3 Angela and Ben each have a monthly cell phone bill. Angela’s monthly bill is represented by the function 𝑦=0.15𝑥+49, where 𝑥 represents the minutes and 𝑦 represents the cost. Ben’s monthly cost is shown in the graph.

Example 3a Angela 𝑦=0.15𝑥+49 Compare the y-intercepts and rate of change. Ben has a greater initial cost 80−60 200−0 Angela pays more per minute than Ben. Ben =0.10

Example 3b What will the monthly cost for Angela and Ben for 200 minutes? Angela Ben 𝑦=0.15𝑥+49 𝑦=0.15 200 +49 𝑦=79 $79 Find 200 mins on the graph. $80

The number of new movies a store receives can be represented by the function 𝑚=7𝑤+2, where 𝑚 represents the number of movies and 𝑤 represents the number of weeks. The number of games the same store receives is shown in the table. Compare the functions’ y-intercepts and constant rates of change. How many movies and games will the store have in week 6?

Example 4 Write an equation for the graph 45−35 30−10 𝑦= 1 2 𝑥+30 Lorena’s mother needs to rent a truck to move some furniture. The cost to rent a truck from two different companies is shown in the table and graph. Which company should she use to rent the truck for 40 miles? Write an equation for the graph 45−35 30−10 𝑦= 1 2 𝑥+30 So, she should use Cross Town Movers. = 10 20 = 1 2 + 𝟏𝟎 + 𝟐𝟓 𝟒𝟎 𝟏𝟎𝟎

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Compare Properties of Functions Chapter 4.5 Compare Properties of Functions

Real-World Link Turn to page 309 in your workbook!

Example 1 A zebra’s main predator is a lion. Lions can run at a speed of 53 feet per second over short distances. The graph shows the speed of a zebra. Compare their speeds. 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒

A certain car has a gas mileage of 22 miles per gallon A certain car has a gas mileage of 22 miles per gallon. The gas mileage of a certain sport utility vehicle is represented by the function shown. Compare their gas mileage. 𝑚𝑖𝑙𝑒𝑠 𝑔𝑎𝑙𝑙𝑜𝑛𝑠

Example 2 The function 𝑚=140ℎ, where 𝑚 is the miles traveled in ℎ hours, represents the distance traveled of the first Japanese high speed train. The distance traveled of a high speed train operating today in China is shown in the table. Assume the relationship between the two quantities is linear.

Example 2a Japanese Train 𝑚=140ℎ Compare the functions y-intercepts and constant rates of change. Chinese Train + + + +

Example 2b If you ride each train for 5 hours, how far will you travel on each? Japanese Chinese

Example 3 Angela and Ben each have a monthly cell phone bill. Angela’s monthly bill is represented by the function 𝑦=0.15𝑥+49, where 𝑥 represents the minutes and 𝑦 represents the cost. Ben’s monthly cost is shown in the graph.

Example 3a Angela 𝑦=0.15𝑥+49 Compare the y-intercepts and rate of change. Ben

Example 3b What will the monthly cost for Angela and Ben for 200 minutes? Angela Ben 𝑦=0.15𝑥+49

The number of new movies a store receives can be represented by the function 𝑚=7𝑤+2, where 𝑚 represents the number of movies and 𝑤 represents the number of weeks. The number of games the same store receives is shown in the table. Compare the functions’ y-intercepts and constant rates of change. How many movies and games will the store have in week 6?

Example 4 Write an equation for the graph + + Lorena’s mother needs to rent a truck to move some furniture. The cost to rent a truck from two different companies is shown in the table and graph. Which company should she use to rent the truck for 40 miles? Write an equation for the graph + +

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