Determining the Key Features of Function Graphs
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Determining the Key Features of Function
Graphs
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The Key Features of Function Graphs - Preview Domain and Range x-intercepts and y-intercepts Intervals of increasing, decreasing, and
constant behavior Parent Equations Maxima and Minima
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Domain
To find the domain of the graph _____________________ of the graph
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Determining Domain - Symbols →
→
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Determining Domain1. Start at the origin2.
3. Return to the origin4.
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Examples
Domain:Domain:
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Example
Domain:
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Determining Domain - Infinity
Domain:
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Examples
Domain: Domain:
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Your Turn: In the purple Precalculus textbooks,
complete problems 3, 7, and find the domain of 9 and 10 on pg. 160
3. 7.
9. 10.
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Range
To find the range of the graph _____ _________________of the graph
We also use open and closed circles for the range
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Determining Range1. Start at the origin2.
3. Return to the origin4.
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Examples
Range: Range:
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Examples
Range: Range:
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Your Turn: In the purple Precalculus textbooks,
complete problems 4, 8, and find the range of 9 and 10 on pg. 160
4. 8.
9. 10.
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X-Intercepts Has many names:
x-intercept Roots Zeros
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Examples
x-intercepts: x-intercepts:
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Y-Intercepts
y-intercepts: y-intercepts:
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Seek and Solve!!!
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Types of Function Behavior 3 types:
Increasing Decreasing Constant
When determining the type of behavior, ____________________________________________________________________
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Roller Coasters!!!
Fujiyama in Japan
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Types of Behavior – Increasing Direct Relationship
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Types of Behavior – Constant
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Types of Behavior – Decreasing Inverse Relationship
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Identifying Intervals of Behavior
Increasing: [0, 4)
The y-values are increasing
when the x-values are between 0 inclusive and 4 exclusive
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Identifying Intervals of Behavior Increasing:
Constant:
Decreasing:
x
1
1
y
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Identifying Intervals of Behavior, cont. Increasing:
Constant:
Decreasing:-1-3
y
x
Don’t get distracted by the arrows! Even though both of the arrows point “up”, the graph isn’t increasing at both ends of the graph!
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Your Turn: Complete problems 1 – 4 on The Key
Features of Function Graphs – Part II handout.
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1.
2.
3.
4.
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What do you think of when you hear the word parent?
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Parent Function Flipbook
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Parent Function The most basic form of a type of function Determines the general shape of the
graph
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Basic Types of Parent Functions1. Linear2. Absolute Value3. Greatest Integer4. Quadratic
5. Cubic6. Square Root7. Cube Root8. Reciprocal
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Identifying Parent Equations From Graphs:
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Examples
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Your Turn: Complete problems 5 – 12 on The Key
Features of Function Graphs handout
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Maximum (Maxima) and Minimum (Minima) Points
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Identifying Minimum and Maximum Points
You can have any combination of min and max points
Minimum: Maximum:
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Examples
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Your Turn: Complete problems 1 – 6 on The Key
Features of Function Graphs – Part III handout.
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Reminder: Find f(#) and Find f(x) = x
Find f(#) Find the value of f(x)
when x equals #. Solve for f(x) or y!
Find f(x) = # Find the value
of x when f(x) equals #.
Solve for x!
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Evaluating Graphs of Functions – Find f(#)
1.
2.
f(1) = f(–2) =
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Evaluating Graphs of Functions – Find f(x) = #
1.
2.
f(x) = –2 f(x) = 2
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Example
1. Find f(1)
2. Find f(–0.5)
3. Find f(x) = 0
4. Find f(x) = –5
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Your Turn: Complete Parts A – D for problems 7 – 14
on The Key Features of Function Graphs – Part III handout.