Algebra
A Function Preview
Function #1
Verbal/Algebraic
For drivers aged x years, a study found that the driver’s reaction time to a visual stimulus such as a traffic light can be modeled by the equation R = .0005x2 - .023x + 22, where R is the reaction time in milliseconds.
Input/Output
In this function, ______depends on ______.
Numerical
Complete the following table to represent the function numerically.
x / R16
26
36
46
56
66
76
Graphical
Use the numerical representation of the function to create a graphical representation of the function.
Function #2
Verbal/Algebraic
The relationship between the profit made at a rock concert and the ticket price for the concert is represented by the equation P = -250x2 + 4000x – 7500, where P is the profit in dollars and x is the ticket price in dollars.
Input/Output
In this function, ______depends on ______.
Numerical
Complete the following table to represent the function numerically.
x / P0
2
4
6
8
10
12
Graphical
Use the numerical representation of the function to create a graphical representation of the function.
Function #3
Verbal/Algebraic
If you were to invest $500 in a savings account that earns 8% interest per year, the overall balance of the account can be represented by the equation B = 500(1.08)x, where B is the balance of the account in dollars, and x is the number of years that the money has been in the account.
Input/Output
In this function, ______depends on ______.
Numerical
Complete the following table to represent the function numerically.
x / B0
10
20
30
40
50
60
Graphical
Use the numerical representation of the function to create a graphical representation of the function.
Function #4
Verbal/Algebraic
When a drug such as aspirin is absorbed into the bloodstream, the body naturally breaks the drug down and eliminates it from the bloodstream. Suppose that 500 milligrams of aspirin are digested by a human being, and that the equation Q = 500(.95)x gives the quantity of aspirin, Q in milligrams, in the bloodstream x minutes after injection.
Input/Output
In this function, ______depends on ______.
Numerical
Complete the following table to represent the function numerically.
x / Q0
30
60
90
120
150
180
Graphical
Use the numerical representation of the function to create a graphical representation of the function.
Function #5
Verbal/Algebraic
Julia is the manager of a concession stand that sells, among other things, drinks from a soda fountain. Julia noticed that if she raised the price of a 20 oz. drink, she sold less drinks in a day. The number of drinks that Julia is able to sell is given by the function N = 300 - .85p, where N is the number of drinks sold per day and p is the price of the drink in cents.
Input/Output
In this function, ______depends on ______.
Numerical
Complete the following table to represent the function numerically.
p / N0
25
50
75
100
125
150
Graphical
Use the numerical representation of the function to create a graphical representation of the function.
Function #6
Verbal/Algebraic
Barry has a part time job collecting credit card applications for a major company. He sets his booth up on weekends at sporting events and shopping centers to try to entice people to sign up for a credit card. Barry’s daily pay can be described by the function P = 5n + 20, where P is his daily pay in dollars and n is the number of applications he collects in a day.
Input/Output
In this function, ______depends on ______.
Numerical
Complete the following table to represent the function numerically.
n / P0
5
10
15
20
25
30
Graphical
Use the numerical representation of the function to create a graphical representation of the function.
Activity Summary
As each group is presenting their function, write down the equation that they present and a sketch of the graph that they present. Make sure that you label your axes with the names of the variables for each function.
Group #1 Group #2
Equation: Equation:
Group #3 Group #4
Equation: Equation:
Group #5 Group #6
Equation: Equation:
- Classify the functions into pairs or groups that seem to be similar to one other? Describe your reasoning for classifying the functions as you did.
For Example: I think that function #1 and #4 are similar because…