SWBAT: Write a function based on a given relation.
Lesson 5-5
Do Now:
1) Determine whether the relation is a function. If yes, state the domain and range as an
inequality.
a)
b)
c)
Do Now continues on next page
d)
SWBAT: Write a function based on a given relation.
Lesson 5-5
e)
f)
Evaluate the given functions
If f(x) = 4x – 2, find:
f(5) =
f(-1) =
SWBAT: Write a function based on a given relation.
Lesson 5-5
Identifying Independent and Dependent Variables
The variable that represents the input values of a function is the independent variable
because it can be any value in the domain. The variable that represents the output values of a
function is the dependent variable because it depends on the value of the independent
variable. When an equation represents a function, the dependent variable is defined in terms
of the independent variable. The statement “y is a function of x” means that y varies
depending on the value of x.
1)
The function T(m) = 19m + 65 represents the temperature t (in degrees Fahrenheit) of an
oven after preheating for m minutes.
a) Identify the independent and dependent variables
b) A recipe calls for an oven temperature of 350°F. Describe the domain and range of the
function.
2)
The function f(x) = 3.5x + 2.8 represents
the cost y
(in dollars) of a taxi ride of x miles.
a) Identify the independent and dependent
variables
b) You have enough money to travel at most
20 miles in the taxi. Find the domain and
range of the function.
SWBAT: Write a function based on a given relation.
Lesson 5-5
Write Function Rules from a Description
3) A doctor charges $200 per visit. Write a function rule for this situation.
a) Identify and label the independent and dependent variables. (Include units)
Dependent Variable f(x)
What will the equation be about?
Independent Variable (x)
What does f depend on?
b) Write a function rule.
c) Identify and explain an appropriate domain
d) If the doctor has 75 office visits in one week, how much did the doctor earn?
4) A car travels at a constant rate of 65 miles per hour.
a) Identify and label the independent and dependent variables. (Include units)
Dependent Variable f(x)
What will the equation be about?
Independent Variable (x)
What does f depend on?
b) Write a function rule.
c) Identify and explain an appropriate domain
d) If the car travels 780 miles how many hours did it take?
SWBAT: Write a function based on a given relation.
Lesson 5-5
5)
Mike’s new car can get 30 miles per gallon of gas. The tank can hold up to 10 gallons of gas.
a) Identify and label the independent and dependent variables. (Include units)
Dependent Variable f(x)
What will the equation be about?
b) Write a function rule.
c) Identify and explain an appropriate domain
d) What is the range for this function?
Check for Understanding
Independent Variable (x)
What does f depend on?
SWBAT: Write a function based on a given relation.
Lesson 5-5
Summary
SWBAT: Write a function based on a given relation.
Lesson 5-5
LESSON PRACTICE
SWBAT: Write a function based on a given relation.
Lesson 5-5
SWBAT: Write a function based on a given relation.
Lesson 5-5
Homework Unit 5 – Day 5
Page 249 # 5, 6, 7, 8, 18, 19, 21, 22, 28
SWBAT: Write a function based on a given relation.
Lesson 5-5