1. 2.1 What is a function?
Day 2
1 Corinthians 10:13 No temptation has overtaken you that
is not common to man. God is faithful, and he will not let
you be tempted beyond your ability, but with the
temptation he will also provide the way of escape, that you
may be able to endure it.

2. The Rule of Four
There are four ways to represent a function:

3. The Rule of Four
There are four ways to represent a function:
Verbal (in English)

4. The Rule of Four
There are four ways to represent a function:
Verbal (in English)
Algebraic (formula, equation, etc.)

5. The Rule of Four
There are four ways to represent a function:
Verbal (in English)
Algebraic (formula, equation, etc.)
Graphic (a graph ...)

6. The Rule of Four
There are four ways to represent a function:
Verbal (in English)
Algebraic (formula, equation, etc.)
Graphic (a graph ...)
Numeric (a table of values)

7. Answer these questions with your group:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x

8. Answer these questions with your group:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x
a) How long does it take the car to travel the stretch if
the car is going 10 mph over?

9. Answer these questions with your group:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x
a) How long does it take the car to travel the stretch if
the car is going 10 mph over?
b) How long does it take the car to travel the stretch if it
goes the speed limit?

10. Answer these questions with your group:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x
a) How long does it take the car to travel the stretch if
the car is going 10 mph over?
b) How long does it take the car to travel the stretch if it
goes the speed limit?
c) Make a table of values giving the travel time for x
values from 0 to 40 mph. What can be concluded from
the table?

11. Answer these questions with your group:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x
a) How long does it take the car to travel the stretch if
the car is going 10 mph over?
b) How long does it take the car to travel the stretch if it
goes the speed limit?
c) Make a table of values giving the travel time for x
values from 0 to 40 mph. What can be concluded from
the table?
d) Look at the graph of this function and discuss.

12. Answers:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x

13. Answers:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x
a) How long does it take the car to travel the stretch if
the car is going 10 mph over?
100 100
t(10) = = ≈ 1.18 hrs.
75 + 10 85

14. Answers:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x
a) How long does it take the car to travel the stretch if
the car is going 10 mph over?
100 100
t(10) = = ≈ 1.18 hrs.
75 + 10 85
b) How long does it take the car to travel the stretch if it
goes the speed limit?
100 100
t(0) = = ≈ 1.33 hrs.
75 + 0 75

15. Answers:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x

16. Answers:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x
c) Make a table of values giving the travel time for x
values from 0 to 40 mph. What can be concluded from
the table? (do this on the overhead calculator)

17. Answers:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x
c) Make a table of values giving the travel time for x
values from 0 to 40 mph. What can be concluded from
the table? (do this on the overhead calculator)
The more you speed, the faster you get there but at
some point the change in time isn’t that much.

18. Answers:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x
c) Make a table of values giving the travel time for x
values from 0 to 40 mph. What can be concluded from
the table? (do this on the overhead calculator)
The more you speed, the faster you get there but at
some point the change in time isn’t that much.
d) Look at the graph of this function and discuss.
(do this on the overhead calculator)

19. Answers:
If the speed limit on a 100 mile stretch of road is 75
mph, then the amount of time it takes a car going x mph
over the limit is given by t(x) = 100
75 + x
c) Make a table of values giving the travel time for x
values from 0 to 40 mph. What can be concluded from
the table? (do this on the overhead calculator)
The more you speed, the faster you get there but at
some point the change in time isn’t that much.
d) Look at the graph of this function and discuss.
(do this on the overhead calculator)
Discuss the decay curve and the relation to the table of
values from part c; other observations?

20. Do HW #2
“Courage is doing what you’re afraid to do. There
can be no courage unless you’re scared.”
Eddie Rickenbacher