Transcript 1. For ƒ(x)
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Function Notation
Objectives
Write functions using function notation.
Evaluate and graph functions.
Holt Algebra 2
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Function Notation
1. For ƒ(x) = 5x + 3
ƒ(-1)=
Evaluate ƒ(0)=
and ƒ(–2) =
2. For the graph, evaluate ƒ(0),
ƒ(.5) ,
and ƒ(–2).
3. Evaluate ƒ(0), ƒ
, and ƒ(–2) for ƒ(x) = x2 – 4x
4. Graph the function f(x) = 2x + 1.
5. A painter charges $200 plus $25 for each can of paint used.
a. Write a function to represent the total charge for a certain
number of cans of paint.
b. Evaluate f(4), and state what it represents?
Holt Algebra 2
1-7
Function Notation
The function described by ƒ(x) = 5x + 3 is the same
as the function described by y = 5x + 3. And both of
these functions are the same as the set of ordered
pairs (x, 5x+ 3).
y = 5x + 3
(x, y)
ƒ(x) = 5x + 3
(x, ƒ(x))
Holt Algebra 2
(x, 5x + 3)
Notice that y = ƒ(x)
(x, 5x + 3) for each x.
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Function Notation
Example 1: Evaluating Functions
For each function, evaluate ƒ(0), ƒ
ƒ(–2).
ƒ(x) = 8 + 4x
Substitute each value for x and evaluate.
ƒ(0) = 8 + 4(0) = 8
ƒ
=8+4
= 10
ƒ(–2) = 8 + 4(–2) = 0
Holt Algebra 2
, and
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Function Notation
Notes #1: Notation and Evaluating Functions
ƒ(x) = 5x + 3
ƒ of x equals 5 times x plus 3.
f(1)= 8 for f(x) = 5x + 3
(1, 8) for y = 5x + 3
For the function, evaluate ƒ(0)=
ƒ(-1)=
and ƒ(–2) =
Holt Algebra 2
1-7
Function Notation
Notes #2: Evaluating Functions
For each function, evaluate ƒ(0), ƒ
ƒ(–2).
Use the graph to find the
corresponding y-value for
each x-value.
ƒ(0) = 3
ƒ
=0
ƒ(–2) = 4
Holt Algebra 2
, and
1-7
Function Notation
Notes #3: Evaluating Functions
For each function, evaluate ƒ(0), ƒ
ƒ(–2).
ƒ(x) = x2 – 4x
Holt Algebra 2
, and
1-7
Function Notation
Example 2A: Graphing Functions
Graph the function.
{(0, 4), (1, 5), (2, 6), (3, 7), (4, 8)}
Graph the points.
Do not connect the
points because the
values between the
given points have
not been defined.
Holt Algebra 2
1-7
Function Notation
Example 2B: Graphing Functions
Graph the function f(x) = 3x – 1.
Make a table.
Graph the points.
x
3x – 1
f(x)
–1
3(– 1) – 1
–4
0
3(0) – 1
–1
1
3(1) – 1
2
Connect the points with a line because
the function is defined for all real numbers.
Holt Algebra 2
1-7
Function Notation
Example 2C
Graph the function.
3 5 7 9
2 6 10
Graph the points.
Do not connect the
points because the
values between the
given points have not
been defined.
Holt Algebra 2
1-7
Function Notation
Notes #4: Graphing Functions
Graph the function f(x) = 2x + 1.
Graph the points.
Make a table.
x
2x + 1
f(x)
–1
2(– 1) + 1
–1
0
2(0) + 1
1
1
2(1) + 1
3
Connect the points with a line because
the function is defined for all real numbers.
Holt Algebra 2
1-7
Function Notation
Example 3A: Function Application
A local photo shop will develop and print the
photos from a disposable camera for $0.27 per
print.
Write a function to represent the cost of photo
processing.
Let x be the number of photos and let f be the total cost
of the photo processing in dollars.
Identify the variables.
Cost depends on the number of photos processed
Cost = 0.27 number of photos processed
f(x) = 0.27x
Holt Algebra 2
Replace the words with expressions.
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Function Notation
Notes 3B: Function Application
A local photo shop will develop and print the
photos from a disposable camera for $0.27 per
print.
What is the value of the function for an input
of 24, and what does it represent?
f(24) = 0.27(24)
Substitute 24 of x and simplify.
= 6.48
The value of the function for an input of 24 is 6.48.
This means that it costs $6.48 to develop 24 photos.
Holt Algebra 2
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Function Notation
Notes #5: Function Application
A painter charges $200 plus $25 for each can of
paint used.
a. Write a function to represent the total charge
for a certain number of cans of paint.
t(c) = 200 + 25c
b. What is the value of the function for an input
of 4, and what does it represent?
300; total charge in dollars if 4 cans of
paint are used.
Holt Algebra 2