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lab2_rational_functions_and_time_passed_during_a_trip.pdf

Rational Functions and Time Passed During a Trip

You will be driving from Central Texas College in Killeen to a town in Texas and looking at the effect of

driving the distance at different speeds.

Choose any city/town in Texas that is at least 50 miles from Central Texas College in Killeen, TX, by road.

Go to Google Maps (https://maps.google.com) and find directions from CTC to the city/town of your

choice.

Take a screenshot of the directions like you did for Lab 1, which you will upload in Blackboard when you

turn in the lab. Make sure that your screenshot shows the starting and ending address. Note the

distance of the trip in miles:

Distance One Way: _______________ miles Round-Trip Distance (x2): ___________________ miles

You drive from CTC in Killeen to your town of choice. After 3 hours at your town of choice, you receive

a phone call and immediately return to CTC in Killeen. Calculate the total time for the round-trip for the

different speeds (not necessarily realistic, legal, or even safe speeds). Remember the equation

distance = rate ∗ time. We can rearrange the equation to make time = distance

rate and that you are going

round-trip. What effect does spending 3 hours there have on the total time?

Speed 0.5 mph 1 mph 2 mph 10 mph 20 mph 40 mph 80 mph 160 mph

Total Time

(hours)

Write an equation for the total time of the round trip 𝑦 as a function of the speed 𝑥. (Don’t forget to

include the 3 hours spent at your destination.

𝑦 = ________________________________________________

Graph your function in an appropriate window. What values of 𝑥 (speed) and 𝑦 (time) make sense in

the context of this problem?

Domain: Range:

Where is the function increasing, decreasing, constant?

Increasing: Decreasing: _____ Constant:

As your speed gets faster, the total time 𝑦 approaches _____________________ because

_________________________________________________________________________.

As your speed gets closer and closer to 0 mph, your total time 𝑦 approaches ______________________

because _________________________________________________________________________.

lab2questions.docx

1. Enter the total  round trip  distance of the trip in miles.

For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

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1 points   

QUESTION 3

1. Enter your answers for the Total Time of the round-trip for the different speeds in the order they appear in the table, separated by commas. Round any decimals to the nearest hundredth.

For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

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4 points   

QUESTION 4

1. Enter your equation for the total time of the round-trip y as a function of the speed x. Make sure your answer starts with "y=".

For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

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QUESTION 5

1. Enter the domain of the function in the context of this lab. (Hint: Do any values of t not make sense for the time of a trip?)

For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

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QUESTION 6

1. Enter the range for the function in the context of this lab. (Hint: Do any values of y not make sense for the distance of a trip?)

For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

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QUESTION 7

1. Enter the values for which the function is increasing, decreasing, and constant.

For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

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QUESTION 8

1. Use Desmos ( https://www.desmos.com/calculator ) to graph your equation. Fix the window to highligh the domain and range that you listed in the lab.  Upload an image/screenshot of the graph of your equation with appropriate values of x and y.  

1. Attach File

3 points   

QUESTION 9

1. Enter your two responses for the corresponding blanks for the following sentence separated by a comma.

As your speed gets faster, the total time approaches __________ because ____________________.

For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

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2 points   

QUESTION 10

1. Enter your two responses for the corresponding blanks for the following sentence separated by a comma.

As your speed gets closer and closer to 0 mph, your total time approaches __________ because ____________________.

For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).