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Key Features of a Graph.pdf

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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?


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• Domain and Range

• xintercepts and yintercepts

• Intervals of increasing, decreasing, and constant behavior

• Parent Equations

• Maxima and Minima



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• 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.



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Don't forget your Including/Excluding Symbols!


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.


Steps for Finding Domain


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Domain:


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Domain:


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Domain:


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Domain:

Warm Up: Find the domain, and explain how you found it.


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Domain: Domain:


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• 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


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• 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.


• Keep moving along the yaxis until you find your highest possible yvalue of the graph. This is your upper bound.


Steps for finding the Range of a Function:


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Range:


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Range:


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Alternative way of finding Range:

Rotate and find domain.


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Alternative way of finding Range:

Rotate and find domain.


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Range: Range:


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Challenge: Find the domain & RANGE of each.


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XIntercepts:

• Where the function crosses the xaxis.

• Has many names:

– Roots

– Zeros

– XIntercepts


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What are the xintercepts of this function?


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What are the xintercepts of this function?


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What are the yintercepts of this function?

What is a yintercept?


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What are the intercepts of this function?Warm Up:


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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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As x is increasing (as we go from left to right)....y is also increasing.


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As x increases, y stays the same (AKA ???).


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As x increases, y is decreasing. This is known as an inverse relationship.


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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.


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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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Identify the intervals for which the function is:

• Increasing

• Decreasing

• Constant


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Identify the intervals for which the function is:

• Increasing

• Decreasing

• Constant


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What do you think of when you hear the word parent?


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Types of Parent Functions

• Linear

• Quadratic

• Cubic

• Square Root

• Cubed Root

• Reciprocal

• Absolute Value


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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


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Absolute Value

y=


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"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


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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).


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Identify the parent functions.

f(x) = 1

x+2


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Identify the parent functions.Peaks or hills are maximum points.

Valleys are your

minimum points.


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Identify the maximum and minimum points.

Maximum:

Minimum:

Write answers in ordered pairs.


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Maximum:

Minimum:



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Maximum:

Minimum:



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Identify the parent functions.

f(x) = 1

x+2


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Key Features of a Graphappohigh.enschool.org/ourpages/auto/2013/1/22/45273314/1...2013/01/22 ·...

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