Introduction to Functions
A relation is given below. {(0, 0), (2, 0.5), (4, 1), (3, 1.5), (4, 2), (5, 1.5), (6, 8)}
Which ordered pair can be removed to make this relation a function? Answer: ( 4, 1) Why would removing this ordered pair make the relation a function? Answer: Every input must be paired with exactly one output.
Determine which of the following are functions. Select all that apply.
Answer: A Answer: D
When given a graph, the vertical line test can be used to determine functionality. Describe the vertical line test and explain the reasons why a graph would, or would not, represent a function.
Answer: If you can draw any vertical line which intersects the graph more than once then the graph does not represent a function. The intersection shows that for a given value of x in the domain there is more than one value of f(x). So this is a one-to-many relation and is not a function because a function must be one-to-one or many-to one.
When comparing prices for activities at a local recreation center, you notice that the center charges different prices on different days of the week. For example, riding a go-kart costs $10 on Saturday and Sunday and $5 on Monday through Friday. Is the cost a function of the activity type? Explain why or why not.
Answer: No, because the activity type is not changing, the only variable in this question (other than the price) is the day of the week, So the price is a function/is affected by the day of the week rather than the activity type.
The altitude of an airplane is represented in the graph below. Is the airplane's altitude a function of time?
Answer: Yes, because any input of time results in only one output of altitude.
The table below represents an object thrown into the air. Is the situation a function?
Answer: Yes, because each input has exactly one output.
Identify which of the following equations represent functions. Select all that apply.
Answer: y = 4x + 13 Answer: y = 3x2 - x - 1
Compare these two scenarios. Which scenario, A or B, represents a function?
Answer: ✔A
Use the vertical line test to determine which graph does not represent a function.
Answer: ✔Graph B
Read the situations below and determine which relationship is not functional. Situation 1: a cell phone bill to the amount of minutes used Situation 2: the perimeter of a square to the length of one of the sides of a square Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned
Situation __________ does not represent a function. Answer: 3 This is because____________________. Answer: The same number of credits cards can have different goals.
