Comparing Functions in the Real World Answers
bus stop, 0 miles from home✔ bus stop, 5 miles from homefriend’s house, 2 miles from homefriend’s house, 3 miles from home
bus stop, 1 mile every 2 minutesbus stop, 2 miles every minute✔ friend’s house, 2 miles every 3 minutesfriend’s house, 3 miles every 2 minutes
from the bus stop is faster, taking 17 minutesfrom the bus stop is faster, taking 24 minutesfrom his friend’s house is faster, taking 15 minutesfrom his friend’s house is faster, taking 22.5 minutes
Seth can also get dropped off at Bus Stop #2, which is closer to his school.Which will get him to school faster? (School is 17 miles away.)
Seth found two new ways to get to school. Which route is faster for Seth, when school is 17 miles away?
What information can be used to compare linear relationships? Explain why.
Linear relationships can be compared using their initial values, or yintercepts, and their rates of change, or slopes. Initial values can tell you which relationship started with a greater value. Comparing slopes can tell you which relationship is rising or falling faster.
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from the bus stop is faster, taking 17 minutesfrom the bus stop is faster, taking 24 minutesfrom his friend’s house is faster, taking 15 minutesfrom his friend’s house is faster, taking 22.5 minutes
Seth can also get dropped off at Bus Stop #2, which is closer to his school.Which will get him to school faster? (School is 17 miles away.)
When comparing functions, such as Seth’s scenarios for travelling to school, will the function with the greatest initial value continue to be the greatest as time increases? Explain why.
No, the function with the greatest initial value will not necessarily remain the greatest as time increases. Whether a function stays "on top" depends on its rate of change (slope) relative to the other functions. Explanation :Initial Value (\(y\)-intercept): This only tells you where the function starts at \(t = 0\).Rate of Change (Slope): This determines how fast the value grows or shrinks over time .Scenarios :Lower Rate of Change: If the function with the higher starting point has a smaller slope (or a negative slope) than another function, the other function will eventually "catch up" and overtake it. Different Function Types: In travel scenarios, one person might start further ahead (higher initial value) but walk slowly, while another person starts at home (zero initial value) but bikes quickly. The biker will eventually pass the walker.
Seth found two new ways to get to school. Which route is faster for Seth, when school is 17 miles away?
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