Chapter 1 Notes
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Transcript of Chapter 1 Notes
Chapter 1 NotesSection 1.3
Graphs of Functions
Graphs of functions are the collections of ___________________
Where x is the ___________of the function, also called the __________ of the function f
And f(x) is the ____________of the function (y-value)
1.3 Notes (continued)• A graph of function f is
shown• Use the picture of f to
determine the domain ______
• Use the picture to determine the range ______
• Use the picture to findf(2) _____f(0) _____f(-1) _____f(4) _____
1.3 Notes (continued)• Finding Domain and range of a function• If• What is the domain?
• What is the range?
• Check your result graphically
1 xxf
1.3 Notes (continued)• Testing of Graphs for Functions• Use the Vertical Line Test
VLT –
Which of the following graphs are functions?
1.3 Notes (continued)• Increasing, Decreasing, or Constant
– A function is __________ on an interval if, for any x1
and x2, in the interval, ________________________– A function is __________on an interval if, for any x1 and x2, in the interval, ________________________– A function is ________ on an interval if, for any x1 and x2, in the interval, __________________– In other words
• Increasing – ____________________• Decreasing – ___________________• Constant – __________________
1.3 Notes (continued)• Shown to the right is
a graph of a function f.
• On what interval(s) is f increasing, decreasing, and/or constant?
• Increasing• Decreasing• Constant
_______ ____________ ______________ _______
f x
1.3 Notes (continued)• Shown to the right is
a graph of a function f(x) = x3-3x
• On what interval(s) is f increasing, decreasing, and/or constant?
• Increasing ______• Decreasing ______• Constant ______
1.3 Notes (continued)Minimums and Maximums
A function’s value f(a) is a called a _________________ of f if there exists an interval (x1,x2) that contains a such that ____________________
A function’s value f(a) is called a ________________of f if there exists an interval (x1,x2) that contains a such that ____________________
1x 2x
xfaf
a
1.3 Notes (continued)• In General, a function can have any
number of relative mins/maxs
• Some functions may have what is called an ABSOLUTE maximum or minimum– Where that particular value of the function is
the maximum or minimum over the entire domain of the function.
1.3 notes (continued)• Finding relative mins/maxs using calculator.• Approximate any relative minimums or
maximums of
64
22
23
xxxh
xxxxf
1.3 Notes (continued)• Sketching a Piecewise graph by hand.
15212
xxxx
xf
1.3 Notes (continued)• Even, Odd, or Neither.• A function is said to be an ________Function if
• Even functions are symmetric about the y-axis• Or, each value of x and it’s opposite (-x) give the
same value of the function.• A function is said to be an ________ Function if
• Odd functions are symmetric about the origin• Or, each value of x and it’s opposite (-x) give the
opposite value of the function.
______ ______
______ ______
1.3 Notes (continued)• Is f(x) even, odd or neither?
• So, • Graphically -
2 4f x x
1.3 Notes (continued)• Is g(x) even, odd or neither?
• So, • Graphically -
3g x x x