M3U1L01 Parent Functions 2p Class Notes .notebook
Math 3, U1, L01, Parent Functions and their Characteristics
Be able to:
Identify, with proper notation, key characteristics of absolute value, quadratic, radical, polynomial exponential, and linear functions.
Know:
Basic function structure and graph of absolute value, quadratic, radical, polynomial exponential, and linear functions
Honors: Describe concavity
Interval Notation
CoolMath.com
August 29, 2016
M3U1L01 Parent Functions 2p Class Notes .notebook
Match Parent Functions (dual screen)
Match Parent Functions (dual screen)
Quadratic
Polynomial
Linear
Radical
Abs.
Value
Exponential
Logarithmic
y = x2
y = |x|
y = log(x)
August 29, 2016
M3U1L01 Parent Functions 2p Class Notes .notebook
August 29, 2016
Range
Domain
o
o
Increasing
Decreasing
(0,1.5)
o
(2,­1)
(­3,­3)
M3U1L01 Parent Functions 2p Class Notes .notebook
Minimums
August 29, 2016
Maximums
(0,1.5)
o
(2,­1)
(­3,­3)
y-intercepts
x-intercepts
(0,1.5)
o
(2,­1)
(­3,­3)
M3U1L01 Parent Functions 2p Class Notes .notebook
Polynomial End Behavior
August 29, 2016
i.e Kinda like..."f(±∞)"
(0,1.5)
o
(2,­1)
(­3,­3)
x interval
(0,∞)
(­∞,0)
even degree odd degree
pos up
pos up
neg down neg down
ditto
opposite
End Behavior Practice
y = 3x2+2x
y = 3x3+2x
y = (.75)x
M3U1L01 Parent Functions 2p Class Notes .notebook
Concavity
August 29, 2016
Honors: Describe concavity
Concave up: The rate of change OF THE SLOPE is
positive.
Concave down: The rate of change OF THE SLOPE
is negative.
Review these three resources on the discussion board.
Math is Fun: Concave Upward and Downward
Paul's Online Math Notes: Definition I
Khan Academy: Analyzing Functions with Calculus: Concavity
x y = x2
-4
-3
-2
-1
Concave up:
0
1
Concave down:
2
3
POI:
4
Δy/Δx
(Δy/Δx)''
M3U1L01 Parent Functions 2p Class Notes .notebook
x y = x3
-4
-3
-2
-1
Concave up:
0
1
Concave down:
2
3
POI:
4
August 29, 2016
Δy/Δx
(Δy/Δx)"
M3U1L01 Parent Functions 2p Class Notes .notebook
August 29, 2016
Math 3 U1 L01 Homework
For each of the seven types of functions introduced in this lesson: Sketch a graph of the parent function and complete the table. Use interval notation and ordered pairs where possible. Use N/A where not applicable.
Linear (use y = x), Absolute Value (use y = |x|), Quadratic (use y = x2), Radical (use y = sqrt(x) ), Polynomial (use y=x3 ­ 4x), Logarithmic (use y = log(x), and Exponential (use y = 10x)
Function:
Domain:
Max's:
Range:
Min's:
Increasing:
x­int:
Decreasing:
y­int:
Concavity:
End Behavior: