lecture 3.1 to 3.2 bt
TRANSCRIPT
Today’s Agenda
Attendance / Announcements
◦ Projects due at Start of Class
◦ Quiz Wednesday
◦ Need Graphing Calculators (TI-83,84,..)
Section 3.1, 3.2
Functions
A function is a rule (think: operation) that assigns an input value to exactly one specific output
f(x) can be thought of as “y”
Examples…before we really define what a function is.
32 xy 32)( xxf
xxy 323 2 ttth 323)( 2
xy 3 xxg 3)(
A function is a rule (think: operation) that assigns an input value to exactly one specific output
inputs outputsf(x)
Domain Range
Determine if each relation is a function or not…
𝐢𝐧𝐩𝐮𝐭 𝒙 9 4 1 0 1 4 9
𝐨𝐮𝐭𝐩𝐮𝐭 𝒚 3 2 1 0 - 1 - 2 - 3
“Functions need to be predictable!”
Determine if each relation is a function or not…
𝐢𝐧𝐩𝐮𝐭 𝒙 -2 -1 0 3 4 6 9
𝐨𝐮𝐭𝐩𝐮𝐭 𝒚 3 2 1 0 1 2 3
Since it is a function, it has a domain and range:
Domain (set of all inputs): { }
Range (set of all outputs): { }
“The Difference Quotient”
The difference quotient for a function f(x) is:
h
xfhxf )()(
Substitute, Subtract, and Simplify
Finding Domains of Functions
The domain of a function is the set of values where the function is defined.
So, to find domains, we need to think about where functions are NOT defined!
Piecewise Functions
01
01)(
2
xx
xxxf
“Pieces of the
Function”
Domain of each piece
A single function, f
Graphing FunctionsMethod 1: Plotting Points (T-Chart)
3)( xxg
Find the domain of
the function, before
making the T-Chart
Reading Graphs of Functions(Similar to what we’ve already done)
1 2 3 4
1
2
3
4
)(xf
)2(f
)1(f
)2(f
)4(f
Reading Graphs of Functions(Similar to what we’ve already done)
1 2 3 4
1
2
3
4
)(xf
xxf ,3)(
xxf ,0)(
Graphing Functions
Determining if a graph is a function
The Vertical Line Test
This is a visual representation of what we did last class…Each input cannot have more than one output (not predictable)