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Determining the Key Features of Function Graphs. 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. Domain. - PowerPoint PPT Presentation
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Determining the Key Features of Function
Graphs
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
Domain
To find the domain of the graph _____________________ of the graph
Determining Domain - Symbols →
→
Determining Domain1. Start at the origin2.
3. Return to the origin4.
Examples
Domain:Domain:
Example
Domain:
Determining Domain - Infinity
Domain:
Examples
Domain: Domain:
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.
Range
To find the range of the graph _____ _________________of the graph
We also use open and closed circles for the range
Determining Range1. Start at the origin2.
3. Return to the origin4.
Examples
Range: Range:
Examples
Range: Range:
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.
X-Intercepts Has many names:
x-intercept Roots Zeros
Examples
x-intercepts: x-intercepts:
Y-Intercepts
y-intercepts: y-intercepts:
Seek and Solve!!!
Types of Function Behavior 3 types:
Increasing Decreasing Constant
When determining the type of behavior, ____________________________________________________________________
Roller Coasters!!!
Fujiyama in Japan
Types of Behavior – Increasing Direct Relationship
Types of Behavior – Constant
Types of Behavior – Decreasing Inverse Relationship
Identifying Intervals of Behavior
Increasing: [0, 4)
The y-values are increasing
when the x-values are between 0 inclusive and 4 exclusive
Identifying Intervals of Behavior Increasing:
Constant:
Decreasing:
x
1
1
y
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!
Your Turn: Complete problems 1 – 4 on The Key
Features of Function Graphs – Part II handout.
1.
2.
3.
4.
What do you think of when you hear the word parent?
Parent Function Flipbook
Parent Function The most basic form of a type of function Determines the general shape of the
graph
Basic Types of Parent Functions1. Linear2. Absolute Value3. Greatest Integer4. Quadratic
5. Cubic6. Square Root7. Cube Root8. Reciprocal
Identifying Parent Equations From Graphs:
Examples
Your Turn: Complete problems 5 – 12 on The Key
Features of Function Graphs handout
Maximum (Maxima) and Minimum (Minima) Points
Identifying Minimum and Maximum Points
You can have any combination of min and max points
Minimum: Maximum:
Examples
Your Turn: Complete problems 1 – 6 on The Key
Features of Function Graphs – Part III handout.
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!
Evaluating Graphs of Functions – Find f(#)
1.
2.
f(1) = f(–2) =
Evaluating Graphs of Functions – Find f(x) = #
1.
2.
f(x) = –2 f(x) = 2
Example
1. Find f(1)
2. Find f(–0.5)
3. Find f(x) = 0
4. Find f(x) = –5
Your Turn: Complete Parts A – D for problems 7 – 14
on The Key Features of Function Graphs – Part III handout.