All about Functions
Evaluating Functions
Linear Functions
Write/Solve Functions
Recursive Rules
100
Mr. Fearing creates a rule for Ms. McKenna. The rule takes Ms. McKenna's input, the last name of a student in the 9th grade, and returns the first name of the student. For instance, Love --> Brazil. Is it a function? Explain.
It is not a function because 2 different students could have the same last name. For example, an input of "Rios" could produce "Brandon," "Jorge," or Michael."
100
If h(x) = x^3 - 5x and f(x) = (x-5)/6 , what is the value of h(-2)?
h(-2) = 2
100
What is the generalized rule that matches the table in figure 1 on your reference sheet?
f(x) = -6x + 5
100
Write the equation that matches this verbal statement: Twice the sum of a number and 3 is 20.
2(x+3)=20
100
Write a recursive rule that has a base case of 4 and each output increases by 7.
4 if x=0 f(n-1) + 7 if x>0
200
Create two tables: one that is a function and one that is not a function. Be prepared to explain why for each table.
Function --> needs to show one output for each input Not a function--> needs to show multiple outputs for at least one input
200
If f(x) = (x - 5)/2 and g(x) = x^3 + x^2 - 2x +5 , what is the value of f(g(-1))?
1
200
What is the constant difference between inputs for the chart in Figure 2?
+0.25 ounces
200
This weekend, The Gap is having a special sale for teachers. All items are 35% off. Ms. McKenna wants to buy a sweater that originally costs $65. How much is the sweater after the discount and a 6.5% sales tax rounded to the nearest dollar?
$45
200
The cost of registering to run a marathon increases 10% each week from the previous week's cost. If the current price is $75, how much will it cost to register in 3 weeks, rounded to the nearest dollar?
$100
300
Draw two graphs: one that is a function and one that is not a function. Be able to explain why for each one.
Function --> passes "vertical line test" ; vertical line crosses only once Not a function --> fails "vertical line test" ; vertical line crosses more than once
300
If f(x) = 3x - 2 and g(x) = x^2 , what is the value of f(f(x)))?
9x - 8
300
Which charts under Figure 4 are linear functions? Be able to explain how you can tell.
A, C, and D ; The differences between consecutive outputs (delta) is the same.
300
A red box movie costs 99 cents to rent for one night. Then, an additional $1.50 is added each day (d) that the movie is late. Write an equation to represent the total cost C of a redbox movie including the late fee.
C = 1.50d + 0.99
300
Write the recursive rule that matches the table in Figure 7.
81, if x=0 f(n-1)/3 if x>0
400
What is the domain of the function f(x) = √x+2 ?
Domain: x can be any number greater than or equal to -2
400
Which of the following will produce the lowest value for the function f(x) = -2x^3 - x^2 - 9 ? f(-2) f(-1) f(0) f(1) f(2)
Answer: f(2) f(-2) = 3 f(-1) =-8 f(0) =-9 f(1) = -12 f(2) = -29
400
The table in figure 3 shows the number of calories burned based on the number of minutes biking. How many calories will be burned after 1.5 hours?
290 calories
400
Mr. Fearing's car gets 35 miles per gallon. Gas currently costs $1.84 cents. Find how much it costs Mr. Fearing to drive 360 miles (round to the nearest cent). Then, write an equation to represent the total cost (C) when Mr. Fearing drives (d) miles.
$18.93 ; C = (d/35) * 1.84
400
Write the linear function that matches the recursive rule in figure 6.
h(n) = -4n +1
500
Write a function that has a domain all real numbers except for 4. What is this function?
One Example: f(x) = 3 / x -4
500
The following equation shows how much money you would save for number of years "t" if you start with 10,000 and the interest rate is 7%. A(t) = 10,000 (1 + 0.07)^t . How much money rounded to the nearest cent will you save after 5 years?
$14,025.52
500
What is the 10th output in the chart in Figure 5?
10b + c
500
A pair of Jordan's is on sale for 15% off. After the discount, a 9.5% tax, and $3 shipping, the shoes costs $87. How much was the original price of the Jordan's rounded to the nearest cent ?
$90.25
500
Megan deposits $15,000 into a savings account that earns 4% interest each year. How much money will be in her account after 5 years, rounded to the nearest dollar?
$18,250
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