Writing Functions
Pg. 249 – 250 #13 – 43(odd)
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Determine a relationship between the x- and
y-values. Write an equation.
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Determine a relationship between the x- and
y-values. Write an equation.
{(1, 3), (2, 6), (3, 9), (4, 12)}
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Using a Table to Write an Equation
Determine a relationship between the x- and
y-values. Write an equation.
x
5
y
1
10 15 20
2
3
4
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Determine a relationship between the x- and
y-values. Write an equation.
{(1, 3), (2, 7), (3, 11), (4, 15)}
x
1
2
3
y
3
7
11 15
4
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
The equation in Example 1 describes a function
because for each x-value (input), there is only one
y-value (output).
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
The input of a function is the ____________
The output of a function is the ___________
The value of the dependent variable
depends on, or is a function of, the value of
the independent variable.
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Helpful Hint
There are several different ways to
describe the variables of a function.
Independent
Variable
x-values
Dependent
Variable
y-values
Domain
Range
Input
Output
x
f(x)
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Identifying Independent and Dependent Variables
A painter must measure a room before
deciding how much paint to buy.
The amount of paint depends on the measurement
of a room.
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Identifying Independent and Dependent Variables
The height of a candle decrease d centimeters
for every hour it burns.
The height of a candle depends on the number of
hours it burns.
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Identifying Independent and Dependent Variables
A company charges $10 per hour to rent a
jackhammer.
The cost to rent a jackhammer depends on
the length of time it is rented.
Dependent variable: cost
Independent variable: time
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
An algebraic expression that defines a function
is a ___________.
The dependent variable is a function of the
independent variable.
y
is
y
=
a function of
f
y = f(x)
x.
(x)
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Writing Functions
Identify the independent and dependent
variables. Write a rule in function notation for
the situation.
A math tutor charges $90 per hour.
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Writing Functions
Identify the independent and dependent
variables. Write a rule in function notation for
the situation.
A fitness center charges a $100 initiation
fee plus $40 per month.
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Evaluating Functions
Evaluate the function for the given input values.
For f(x) = 3x + 2, find f(x) when x = 7 and
when x = –4.
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Evaluating Functions
Evaluate the function for the given input values.
For g(t) = 1.5t – 5, find g(t) when t = 6 and
when t = –2.
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Evaluating Functions
Evaluate the function for the given input values.
For
, find h(r) when r = 600
and when r = –12.
When a function describes a real-world
situation, every real number is not always
reasonable for the domain and range. For
example, a number representing the
length of an object cannot be negative,
and only whole numbers can represent a
number of people.
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Finding the Reasonable Range and Domain of a
Function
Joe has enough money to buy 1, 2, or 3 DVDs
at $15.00 each.
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Substitute the domain values into the function
rule to find the range values.
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
The settings on a space heater are the whole
numbers from 0 to 3. The total of watts used for
each setting is 500 times the setting number.
Write a function rule to describe the number of
watts used for each setting. Find a reasonable
domain and range for the function.
SWBAT: Identify independent and dependent variables. Write an
equation in function notation and evaluate a function for given input
values.
Example 5
There are 4 possible settings 0, 1, 2, and 3, so a
reasonable domain would be {0, 1, 2, 3}.
Substitute these values into the function rule to find
the range values.