Transcript Holt Algebra 1 4-3

4-3 Writing Functions
Warm Up
Identify the independent and dependent
variables in each situation.
1. In the winter, more electricity is used when
the temperature goes down, and less is used
when the temperature rises.
D: amount of electricity
I: temperature
Evaluate each function for the given input
values.
2. For f(x) = 5x, find f(x) when x=6 and when
x=7.5
30 and 37.5
Holt Algebra 1
4-3 Writing Functions
Objectives
Identify independent and dependent
variables.
Write an equation in function notation and
evaluate a function for given input values.
Holt Algebra 1
4-3 Writing Functions
Vocabulary
independent variable
dependent variable
function rule
function notation
Holt Algebra 1
4-3 Writing Functions
Directions:
Determine a relationship between the x- and
y-values. Write an equation.
Holt Algebra 1
4-3 Writing Functions
Example 1
x
5
y
1
10 15 20
2
3
4
Step 1 List possible relationships between the
first x and y-values.
5 – 4 = 1 and
Holt Algebra 1
4-3 Writing Functions
Example 1 Continued
Step 2 Determine which relationship works for the
other x- and y- values.
10 – 4  2
and
15 – 4  3
and
20 – 4  4
and
The value of y is one-fifth,
, of x.
Step 3 Write an equation.
or
The value of y is one-fifth of x.
Holt Algebra 1
4-3 Writing Functions
Example 2
{(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.
1
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
3 = 3 and 1 + 2 = 3
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Example 2 Continued
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
Holt Algebra 1
The value of y is 3 times x.
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The equation in Example 1 describes a function
because for each x-value (input), there is only one
y-value (output).
Holt Algebra 1
4-3 Writing Functions
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.
Holt Algebra 1
4-3 Writing Functions
The dependent variable is a function of the
independent variable.
y
is
y
=
a function of
f
y = f(x)
Holt Algebra 1
x.
(x)
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Directions:
Identify the independent and dependent
variables. Write a rule in function notation for
the situation.
Holt Algebra 1
4-3 Writing Functions
Example 3
A math tutor charges $35 per hour.
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.
Holt Algebra 1
4-3 Writing Functions
Example 4
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 + 100.
Holt Algebra 1
4-3 Writing Functions
Example 5
Steven buys lettuce that costs $1.69/lb.
The total cost depends on how many pounds
of lettuce that Steven buys.
Dependent: total cost
Independent: pounds
Let x represent the number of pounds Steven bought.
The function for cost of the lettuce is f(x) = 1.69x.
Holt Algebra 1
4-3 Writing Functions
Example 6
An amusement park charges a $6.00 parking
fee plus $29.99 per person.
The total cost depends on the number of persons in
the car, plus $6.
Dependent: total cost
Independent: number of persons in the car
Let x represent the number of persons in the car.
The function for the total park cost is
f(x) = 29.99x + 6.
Holt Algebra 1
4-3 Writing Functions
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.
Holt Algebra 1
4-3 Writing Functions
Directions:
Write a function to describe the situation. Find a
reasonable domain and range of the function.
Holt Algebra 1
4-3 Writing Functions
Example 7
Joe has enough money to buy 1, 2, or 3 DVDs
at $15.00 each.
Money spent
f(x)
is
=
$15.00
$15.00
for each
•
DVD.
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}.
Holt Algebra 1
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Example 7 Continued
Substitute the domain values into the function
rule to find the range values.
x
f(x)
1
2
3
15(1) = 15 15(2) = 30 15(3) = 45
A reasonable range for this situation is
{$15, $30, $45}.
Holt Algebra 1
4-3 Writing Functions
Example 8
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.
Number of
watts used
is
500
watts
f(x)
=
500
times
•
the setting #.
x
For each setting, the number of watts is f(x) = 500x watts.
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Example 8 Continued
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
0
f(x)
500(0) =
0
1
500(1) =
500
2
500(2) =
1,000
3
500(3) =
1,500
A reasonable range for this situation is {0, 500,
1,000, 1,500} watts.
Holt Algebra 1
4-3 Writing Functions
Lesson Summary: Part I
Write a rule in function notation for each
situation.
1. A buffet charges $8.95 per person.
independent: number of people
dependent: cost
f(p) = 8.95p
2. A moving company charges $130 for weekly
truck rental plus $1.50 per mile.
independent: miles
dependent: cost
f(m) = 130 + 1.50m
Holt Algebra 1
4-3 Writing Functions
Lesson Summary: Part II
Write a function to describe the situation.
Find a reasonable domain and range for the
function.
5. A theater can be rented for exactly 2, 3, or 4
hours. The cost is a $100 deposit plus $200
per hour.
f(h) = 200h + 100
Domain: {2, 3, 4}
Range: {$500, $700, $900}
Holt Algebra 1