writing functions
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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. - PowerPoint PPT PresentationTRANSCRIPT
Writing FunctionsWriting FunctionsWriting FunctionsWriting Functions
Pg. 249 – 250 #13 – 43(odd)Pg. 249 – 250 #13 – 43(odd)
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
y
5 10 15 20
1 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
y
1 2 3 4
3 7 11 15
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.
IndependentVariable
DependentVariable
x-values 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.
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.
Identifying Independent and Dependent Variables
SWBAT: Identify independent and dependent variables. Write an equation in function notation and evaluate a function for given input values.
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: costIndependent variable: time
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 dependent variable is a function of the independent variable.
y is a function of x.
y = f (x)
y = f(x)
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 ___________.
Identify the independent and dependent variables. Write a rule in function notation for the situation.
A math tutor charges $90 per hour.
Writing Functions
SWBAT: Identify independent and dependent variables. Write an equation in function notation and evaluate a function for given input values.
A fitness center charges a $100 initiation fee plus $40 per month.
Writing Functions
Identify the independent and dependent variables. Write a rule in function notation for the situation.
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.
SWBAT: Identify independent and dependent variables. Write an equation in function notation and evaluate a function for given input values.
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.
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.
There are 4 possible settings 0, 1, 2, and 3, so a reasonable domain would be {0, 1, 2, 3}.
Example 5
Substitute these 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.