Warm-Up

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Warm-Up
Please copy and answer each of the following.
1.
2. Evaluate the function h(x) 7x when x 7.
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Characteristics of Functions

• What is a function?

A function is a relationship between two sets of
numbers the domain and the range.
Each input has exactly one output. (x values
cannot repeat)
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Domain and Range

• Domain - The set that is made up of numbers
  called inputs. (usually x numbers)

• Range - The set that is made up of numbers called
  outputs. (usually y or f(x) numbers)

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Domain and Range

• The set of all inputs of a function.
• If x 1, 2, 3, 4 then they are the inputs.

• The set of all outputs of a function.

f(x) x 1
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Example 1 Table of Values

• Identify the domain and range of the functions
  shown in the table of values.

Domain 2, 3, 4, 7 Range 0,1, 2, 3
Domain 3, 5, 9, 11 Range 8, 10, 16, 24
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Example 2 - Mapping
We can check to see if a table of values
represents a function by mapping the inputs and
outputs.
Input
Output
2 3 4 7
0 1 2 3
This is a function because each input goes to
exactly one output.
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Example 3 - Mapping

• Determine the domain and range and state whether
  it is a function? Support your answer

Domain
Range
This is not a function because the input value 1
maps to 2 different output values, 7 8.
Input Output
3 8
1 8
7 3
1 7
1 3 7
3 7 8
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Example 4 - Function Notation

• We use function notation to write the
  mathematical relationship between the domain and
  range.
• We us f(x) instead of y. the symbol f(x) is read
  as the value of f at x or as f of x.
• Example
• f(x) x 1 is equivalent to y x 1
• f(2) is equivalent to f(2)

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Example 5Function Notation
What is the missing value? a) f(2) _____ b)
f(-4) _____ c) f(x) -4 What is the value of
x? d) f(x) 2 What is the value of x?
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Example 6Function Notation

• Use the graph to determine f(-2) and f(1).
• Determine the value of x for
• f(x) -2.

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Graphs of Functions

• Independent Variable - The input variable We
  refer to this variable as x.
• Dependent Variable The output variable because
  its value depends on the value of the input
  variable. We refer to this variable as y, or in
  function notation, as f(x).

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Example 7

• Lets look at the following relation
• f(x) 2x, where x can be 1, 2, 3, or 4.
• Find the domain and range. Is this relation a
  function?

Input x Output f(x)2x
1
2
3
4
The domain is The range is



Do you remember a way to test if a graph is a
function?
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Example 8Is this graph a function?
Remember the vertical alignment test if you can
draw a vertical line and cross the graph in two
places, then it is not a function.
y
x
This cant be a function because there are two
different y values that go with x0 and x1, etc.

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Example 9

• State the domain and range.

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Example 10

• State the domain and range

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Example 11

• State the domain and range

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Example 12

• State the domain and range

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Example 13

• State the domain and range

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Discrete Function

• A function that is defined only for a set of
  numbers that can be listed, such as the set of
  whole numbers or the set of integers.
• one whose values are represented by specific
  values (appear as points on the graph).

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Continuous Function

• A function that is continuous for all points in
  its domain. (appears as a line on the graph).

You can draw it without lifting your pen from the
paper
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x-intercepts, y-intercepts

• x-intercept- where a graph crosses the x-axis
  (also called the zeros)

• y-intercept where a graph crosses the y-axis