Ch4L3 Functions

Question 1

What is a relation?

What is ordered Pair?

What is domain of a relation?

What is range of a relation?

Answer 1

Relation is any set of ordered pairs. Relation can be represented as table and graph.

Example of order pairs: (1,2),(-2,4), (0,1)…. The first number is x-coordinate, the second is the y-coordinate.

Domain of relation is the set of x-coordinates.

Range of relation is the set of y-coordinates.

Question 2

What is a function?

How to represent a function?

Answer 2

A function is a relation in which every member of the domain(input value) is paired with exactly one member of the range( output value).

You can think of Function just like a calculator, you type in a number as input, then calculator calculates and give another number as output.

A function, as a kind of relation, can be represented as equation, function table,graph, and word statement.

Question 3

How to find the value of a function for a certain number?

example here: f(x) = 15x, how to find f(2)?

note: f(x) should be read as “the function of x”

Answer 3

just replace variable x by the given number in the equation, then you can find the f(x).

example: to find f(2), you replace x by 2,so

f(2) = 15x2

=30

Question 4

Find each function value:

1. f(2) if f(x) =x-4
2. f(12) if . f(x)=1/2x+5

Question 5

Independent Variables can change by itself.

Dependent Variable change because of other variables.

In the function of m =20n, here m represent the amount of money earned and n represents the number of lawns mowed. so in this example

which is the dependent variable?

which is the independent variable?

what does m=20n mean?

Answer 5

independent variable: n

dependent variable:m

equation m= 20n represents “the total money m you can earn for mowing n pieces of lawns”.

Question 6

In the function of d =4.5h, here d represents the distance Ray can walk, 4.5 represent Ray’s speed. h represent how many hours Ray walks.

which is the dependent variable?

which is the independent variable?

what does d=4.5h mean?

Answer 6

independent variable: h

dependent variable:d

equation d=4.5h represents “the total distance d Ray can walk in h hours”.

Question 7

What is the Function Table?

Answer 7

Function Table is one way of representing a function. We organize thing below as a table:

value of input(the domain, or independent variable), calculating expression(how to calculate output value),

and value of output(range, or dependent variable).

Question 8

Make function table for f(x)=x+5.

Then state the domain and the range for this function

Answer 8

the domain is the set of the input value, stated as:

____________________________________

the range is the set of output values, stated as:

_____________________________________

Question 9

Make function table for f(x)=2x-3.

Then state the domain and the range for this function

Answer 9

the domain is the set of the input value, stated as:

____________________________________

the range is the set of output values, stated as:

_____________________________________

Question 10

if f(x) = 2x+1

f(3) = ?

Question 11

A bookstore is selling stamps for $4.5 each. The total sales f(n) is a function of the number of stamps n sold.

1. Which is independent variable, which is dependent variable?
2. what values of domain and range make sense in this case?
3. Write down the function for this case
4. what is the total sale for 5 stamps?

Question 12

if f(x) = x-6

f(4) = ?

Question 13

Make a function table for f(x)=8-x

Answer 13

Question 14

A hot air ballon can hold 90,000 cubic feet of air. It is being inflated at a rate of 6,000 cubic feet per minute. The total cubic feet of air a(t) is a function of the time in minutes t.

1. Which is independent variable, which is dependent variable?
2. what values of domain and range make sense in this case?
3. Write down the function for this case
4. what is the total amount of air after 6 minutes?

Question 18

Summary of what you have learned