1. Objectives Identify independent and dependent variables.
Write an equation in function notation and evaluate a function for given input values.

2. Example 1: 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
Step 1 List possible relationships between the first x and y-values.
Step 2 Write an equation. or

3. Check It Out! Example 1
Determine a relationship between the x- and y-values. Write an equation.
{(1, 3), (2, 6), (3, 9), (4, 12)} x 1 2 3 4 y 3 6 9 12
Step 1 List possible relationships between the first x- and y-values.
Step 2 Write an equation.
y = 3x

4. The input (x values) of a function is the independent variable.
The output (y values) of a function is the dependent variable.
The dependent variable depends on the independent variable.
Ex: Your grade in math depends on your test scores (NOT your test score depend on your math grade)
The y values change BECAUSE the x values change. (Your grade changes because of your test scores)

5. Example 2A: Identifying Independent and Dependent Variables
Identify the independent and dependent variables
in the situation.
A painter must measure a room before deciding how much paint to buy.
Think about what changes based on the other thing
The amount of paint depends on the measurement of a room.
Dependent: amount of paint
Independent: measurement of the room

6. Check It Out! Example 2a
Identify the independent and dependent variable in the situation.
A company charges $10 per hour to rent a leaf blower.
Think about what you are able to change in this problem – the cost or the hours (because you are an independent person)
The cost to rent a leaf blower depends on the length of time it is rented.
Dependent variable: cost
Independent variable: time

7. Example 3A: Writing Functions
Identify the independent and dependent variables. Write a rule in function notation for the situation Instead of y, we write f(x)
A math tutor charges $35 per hour “f of x”
The amount a math tutor charges depends on number of hours.
Dependent: charges
Independent: hours
Let h represent the number of hours of tutoring.
The function for the amount a math tutor charges is f(h) = 35h.

8. Example 3B: 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.
The total cost depends on the number of months, plus $100.
Dependent: total cost
Independent: number of months
Let m represent the number of months
The function for the amount the fitness center charges is f(m) = 40m

9. Example 4A: 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.
f(x) = 3(x) + 2
f(x) = 3(x) + 2
Substitute
7 for x.
Substitute
–4 for x.
f(7) = 3(7) + 2
f(–4) = 3(–4) + 2 =
Simplify.
Simplify.
= –12 + 2
= 23
= –10

10. Check It Out! Example 4a
Evaluate the function for the given input values.
For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3.
h(c) = 2c – 1
h(c) = 2c – 1
h(1) = 2(1) – 1
h(–3) = 2(–3) – 1
= 2 – 1
= –6 – 1
= 1
= –7

11. Example 5: Finding the Reasonable Range and Domain of a Function
Joe has enough money to buy 1, 2, or 3 DVDs at $15.00 each.
Write a function to describe the situation. Find a reasonable domain and range of the function.
Money spent
is $ for each DVD.
f(x) = $ • x
If Joe buys x DVDs, he will spend f(x) = 15x dollars.
Joe only has enough money to purchase 1, 2, or 3 DVDs. A reasonable domain is {1, 2, 3}.

12. Check It Out! Example 5
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.
Number of
watts used
is times the setting #.
watts
f(x) = • x
For each setting, the number of watts is f(x) = 500x watts.

13. Assignment: Pg 249 (3-25 odd)