Radical Operations
(DM 1/6) Notes pgs 3-6
(DM 1/6) Notes pgs 3-6
Radical Equations
(DM 1/13) Notes pgs 9-10
(DM 1/13) Notes pgs 9-10
Parent Function Transformations
(DM 1/15) Notes pg 15
(DM 1/15) Notes pg 15
Graphing Transformations
(DM 1/20) Notes 13-14
(DM 1/20) Notes 13-14
Function Characteristics
(DM 1/15) Notes 13-14
(DM 1/15) Notes 13-14
100
sqrt(16x^4y^12z^7
4x^2y^6z^3sqrtz
100
sqrt(5x+6)=9
x=15
100
Absolute Value
Shift Left 4
Shift Down 2
y=|x+4|-2
100
Identify 3 points on the graph...
y=(x-2)^2+1
(1,2)
(2,1)
(3,2)
100
Identify the end behavior:
x->-oo, y->
x->oo, y->
x->-oo, y->oo
x->oo, y->-oo
200
(3-sqrt7)^2
16-6sqrt7
200
sqrt(12x-8)+7=15
x=6
200
Cube Root
Shift Right 4
Shift Up 3
Reflection Across X-Axis
y=-root3(x-4)+3
200
Identify 3 points on the graph...
y=3(x+1)^3
(0,3)
(-1,0)
(-2,-3)
200
Identify relative minimums and maximums:
None (it never changes direction)
300
sqrt(72x^3)/sqrt(6x^2)
2sqrt(3x)
300
sqrt(2x-15)+5=6
x=8
300
Linear
Vertical Stretch of 3.
Shift Left 2.
Reflection Over X-Axis.
y=-3(x+2)
300
Identify 3 points on the graph...
y=-abs(x+5)+2
(-4,1)
(-5,2)
(-6,1)
300
Identify the domain and range.
Domain:
All Real Numbers
Range:
[0,oo)
400
sqrt(98x^8y^6)/sqrt(2x^2y)
7x^3y^2sqrty
400
sqrt(x-2)=x-4
x=6
400
Cubic
Vertical Shrink of 2/3
Shifts Down 70.5
Opens Up
y=2/3x^3-70.5
400
Identify 3 points on the graph...
y=-2root3(x+4)+5
(-3,3)
(-4,5)
(-5,7)
400
Identify the domain and range:
Domain:
[1,oo)
Range:
[2,oo)
500
(5-4sqrtx)^2
25-40sqrtx+16x
500
sqrt(21-5x)=x-3
x=4
500
Exponential Function with a Base of 2
Vertical Shrink of 1/2
Shift Up 2.3
Shift Right 45.8
Reflects Over X-Axis
y=-1/2(2)^(x-45.8)+2.3
500
Identify 3 points on the graph...
y=-sqrt(x-3)+3
(3,3)
(4,2)
(7,1)
500
Identify the relative mins and maxes:
Relative Minimums:
(-1,-4) & (1,-4)
Relative Maximums:
(0,-3)