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Key Features of a Graph.pdf
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January 30, 2013
Key Features of a Graph
Warm Up
What do you think the key features are of a graph? Write them down.
EQ: What are the key features of graphs? How do I find them?
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a Graph
• Domain and Range
• xintercepts and yintercepts
• Intervals of increasing, decreasing, and constant behavior
• Parent Equations
• Maxima and Minima
EQ: What are the key features of graphs? How do I find them?
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a Graph
• We already know that domain is the set of all xvalues (input values), and we know how to find this algebraically (like we did in class yesterday).
• Now we are going to find the domain by looking at the graph of a function.
EQ: What are the key features of graphs? How do I find them?
Key Features of a Graph.pdf
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Key Features of a Graph
Don't forget your Including/Excluding Symbols!
EQ: What are the key features of graphs? How do I find them?
Including Excluding
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Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
• Start at the far left of the graph. (Just like we read...left to right)
• Move along the xaxis until you find the lowest possible xvalue of the graph. This is your lower bound.
– Note if you have a open circle or a closed circle.
• Keep moving along the xaxis until you find your highest possible xvalue of the graph. This is your upper bound.
– Note if you have a open circle or a closed circle.
Steps for Finding Domain
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Domain:
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Domain:
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Domain:
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Domain:
Warm Up: Find the domain, and explain how you found it.
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Domain: Domain:
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
• The set of all possible output or yvalues
• To find the range of the graph we look at the yaxis of the graph
• We also use open and closed circles for the range
Range
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
• Start at the bottom of the graph.
• Move along the yaxis until you find the lowest possible yvalue of the graph. This is your lower bound.
– Note if you have a open circle or a closed circle.
• Keep moving along the yaxis until you find your highest possible yvalue of the graph. This is your upper bound.
– Note if you have a open circle or a closed circle.
Steps for finding the Range of a Function:
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Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Range:
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Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Range:
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Alternative way of finding Range:
Rotate and find domain.
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Alternative way of finding Range:
Rotate and find domain.
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Range: Range:
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Challenge: Find the domain & RANGE of each.
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
XIntercepts:
• Where the function crosses the xaxis.
• Has many names:
– Roots
– Zeros
– XIntercepts
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
What are the xintercepts of this function?
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
What are the xintercepts of this function?
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
What are the yintercepts of this function?
What is a yintercept?
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
What are the intercepts of this function?Warm Up:
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Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Types of Function Behavior:• There are 3 Types of Function Behavior:
– Increasing
– Decreasing
– Constant
• Just like the other things we have done in class you always read this from LEFT TO RIGHT!!!
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
As x is increasing (as we go from left to right)....y is also increasing.
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
As x increases, y stays the same (AKA ???).
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
As x increases, y is decreasing. This is known as an inverse relationship.
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Identifying Intervals of Behavior Process:
• We are going to use interval notation just like we did for finding the Domain & Range.
• The interval measures the xvalues.
• The description of the behavior gives the yvalues.
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Identifying Intervals of Behavior Process:
• We are going to use interval notation just like we did for finding the Domain & Range.
• The interval measures the xvalues.
• The description of the behavior gives the yvalues.
Increasing: [0,4)The yvalues
are increasing.
The xvalues are between 0 and 4 including 0, but not including 4.
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Identify the intervals for which the function is:
• Increasing
• Decreasing
• Constant
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Identify the intervals for which the function is:
• Increasing
• Decreasing
• Constant
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January 30, 2013
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Key Features of a Graph.pdf
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Key Features of a Graph.pdf
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January 30, 2013
Key Features of a Graph.pdf
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Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
What do you think of when you hear the word parent?
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Types of Parent Functions
• Linear
• Quadratic
• Cubic
• Square Root
• Cubed Root
• Reciprocal
• Absolute Value
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January 30, 2013
Linear y=x
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Quadratic y=x2
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Cubicy=x3
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Square Rooty=√x
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Cubed Root
y=∛x
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Reciprocaly=1/x
Key Features of a Graph.pdf
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January 30, 2013
Absolute Value
y=
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
"Baby Functions"
• Look and behave similarly to their parent functions.
• To get a “baby” functions, add, subtract, multiply, and/or divide parent equations by (generally) constants
– f(x) = x2 f(x) = 5x2 – 14
– f(x) = 1/x f(x) = 4(2/x)
– f(x) = x3 f(x) = 2x3 + 4x2 – x + 2
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
To identify what a function's "Parent" is:
• Look for obvious symbols such as square root signs, cubed root signs, absolute value signs, and fractions with an x in the denominator.
• If there are no crazy symbols then look for the highest exponent that there is in the problem. (the degree tells you what type of function it is if there are no other crazies involved).
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Identify the parent functions.
f(x) = 1
x+2
Key Features of a Graph.pdf
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January 30, 2013
EQ: What are the key features of graphs? How do I find them?
EQ: What are the key features of graphs? How do I find them?
Key Features of a Graph.pdf
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January 30, 2013
EQ: What are the key features of graphs? How do I find them?
EQ: What are the key features of graphs? How do I find them?
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Identify the parent functions.Peaks or hills are maximum points.
Valleys are your
minimum points.
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Identify the maximum and minimum points.
Maximum:
Minimum:
Write answers in ordered pairs.
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Identify the maximum and minimum points.
Maximum:
Minimum:
Write answers in ordered pairs.
Key Features of a Graph.pdf
56
January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Identify the maximum and minimum points.
Maximum:
Minimum:
Write answers in ordered pairs.
Key Features of a Graph.pdf
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January 30, 2013
Key Features of a GraphEQ: What are the key features of graphs? How do I find them?
Identify the parent functions.
f(x) = 1
x+2
Key Features of a Graph.pdf
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January 30, 2013
