1. Lesson Objective: I will be able to …
Identify independent and dependent variables
Write an equation in function notation and
evaluate a function for given input values
Language Objective: I will be able to …
Read, write, and listen about vocabulary, key
concepts and examples

2. Example 1: Using a Table to Write an Equation
Page 9
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.
5 – 4 = 1 or
Step 2 Determine which relationship works for the other x-
and y- values.
10 – 4  and or
Step 3 Write an equation.

3. The input of a function is the independent variable.
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The input of a function is the independent variable.
The output of a function is the dependent variable.
The value of the dependent variable depends on, or is a function of, the value of the independent variable.
Examples:
For y = x + 1, the y-value depends on the value of x. If
x = 3, then we can determine that y = = 4.
independent variable: x; dependent variable: y
The amount of a fine for a speeding ticket depends on the
number of miles per hour a person is driving over the speed
limit.
independent variable: number of mph over speed limit;
dependent variable: amount of fine for speeding ticket

4. Example 2: Identifying Independent and Dependent Variables
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Identify the independent and dependent variables in the situation.
A painter must measure a room before deciding how much paint to buy.
The amount of paint depends on the measurement of a room.
independent variable: measurement of the room
dependent variable: amount of paint

5. Helpful Hint
There are several different ways to describe the variables of a function.
Independent
Variable
Dependent
Variable
x-values
y-values
Domain
Range
Input
Output x
f(x)

6. An algebraic expression that defines a function is a function rule.
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An algebraic expression that defines a function is a function rule.
If x is the independent variable and y is the dependent variable, then function notation for y is f(x), read “f of x,” where f names the function.
When an equation in two variables describes a function, you can use function notation to write it.

7. The dependent variable is a function of the independent variable.
y is a function of x.
y = f (x)
y = f(x)

8. Example 3: Writing Functions
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Identify the independent and dependent variables. Write a rule in function notation for the situation.
A math tutor charges $35 per hour.
The amount a math tutor charges depends on number of hours.
independent variable: hours
dependent variable: amount charged
Let h represent the number of hours of tutoring.
The function for the amount a math tutor charges is f(h) = 35h.

9. Example 4: Writing Functions
Page 11
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.
independent variable: number of months
dependent variable: total cost
Let m represent the number of months
The function for the amount the fitness center charges is f(m) = 40m

10. You can think of a function as an input-output machine.x 2
You can think of a function as an input-output machine. 6
function
f(x)=5x 5x 10 30
output

11. Example 5: Evaluating Functions
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Evaluate the function for the given input values.
For g(t) = 1.5t – 5, find g(t) when t = 6 and when t = –2.
g(6) = 1.5(6) – 5
g(–2) = 1.5(–2) – 5
= 9 – 5
= –3 – 5
g(6) = 4
g(-2) = –8

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.

13. Example 6: Finding the Reasonable Range and Domain of a Function
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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}.
Substitute the domain values into the function rule to find the range values. x 1 2 3
f(x)
15(1) = 15
15(2) = 30
15(3) = 45
A reasonable range for this situation is {$15, $30, $45}.

14. Your Turn 1
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Determine a relationship between the x- and y-values. Write an equation. x 1 2 3 4 y 3 6 9 12
Step 1 List possible relationships between the first x- and y-values.
1  3 = 3 and = 3
Step 2 Determine which relationship works for the other x- and y- values.
2 • 3 = 6
3 • 3 = 9
4 • 3 = 12
2 + 2  6
3 + 2  9
4 + 2  12
The value of y is 3 times x.
Step 3 Write an equation.
y = 3x
The value of y is 3 times x.

15. Identify the independent and dependent variables in the situation.
Your Turn 2
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Identify the independent and dependent variables in the situation.
A veterinarian must weigh an animal before determining the amount of medication.
The amount of medication depends on the weight of an animal.
independent variable: weight of animal
dependent variable: amount of medication

16. Steven buys lettuce that costs $1.69/lb.
Your Turn 4
Page 12
Identify the independent and dependent variables. Write a rule in function notation for the situation.
Steven buys lettuce that costs $1.69/lb.
The total cost depends on how many pounds of lettuce that Steven buys.
independent variable: pounds
dependent variable: total cost
Let x represent the number of pounds Steven bought.
The function for cost of the lettuce is f(x) = 1.69x.

17. Evaluate the function for the given input values.
Your Turn 5
Page 13
Evaluate the function for the given input values.
For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4.
Substitute
7 for x.
Substitute
–4 for x.
f(7) = 3(7) + 2
f(–4) = 3(–4) + 2 =
= –12 + 2
f(7)= 23
f(-4) = –10

18. Your Turn 6
Page 14
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.
Number of watts used
is watts times the setting #.
f(x) = • x
For each setting, the number of watts is f(x) = 500x watts.
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. x
f(x) 1 2 3
500(0) =
500(1) =
500
500(2) =
1,000
500(3) =
1,500
A reasonable range for this situation is {0, 500, 1000, 1500}.

19. Classwork
Assignment #13
Holt 4-3 #3-4, 7-11, 26, 33-34, 36