A2 - Section 6.5
Date:___________
Graphing Square Root and Cube Root Functions
(Families of Functions)
Square Root Functions: f ( x)  x
x
-2
-1
0
1
2
3
4
9
16
Given:
f(x)
f ( x) 
x
Domain:_____________
Range:______________
Activity:
1.
2.
Graph f ( x)  x in y1 in bold.
Graph f ( x)  a x when a = -1, ½, 2, and –3 in y2. Compare the graph with f(x) for
each of these.
a)
When a = -1, ______________________________________________
b)
When a = ½,______________________________________________
c)
When a = 2,______________________________________________
d)
When a = -3,______________________________________________
Cube Root Functions: g ( x)  3 x
x
-27
-8
-1
0
1
8
27
f(x)
Given: g ( x)  3 x
Domain:_____________
Range:______________
Activity:
1. Graph g ( x)  3 x in y1 in bold.
2. Graph g ( x)  a 3 x when a = -1, ½, 2, and –3 in y2. Compare the graph with f(x) for
each of these.
a)
When a = -1, _____________________________________________
b)
When a = ½,_____________________________________________
c)
When a = 2,_____________________________________________
d)
When a = -3,_____________________________________________
Graphing by Transformations: (Learn this table!!)
Function Family:
Square Root
y  a ( x  h)  k
(h,k) is the…
Shape of the Graph:
Domain
Range
Cube Root
y  a3 ( x  h)  k
Absolute Value
y  a ( x  h)  k
Quadratic Functions
y  a( x  h)2  k
Cubic Functions
y  a( x  h)3  k
h, the x-coordinate, tells you the _______________________________ from (0, 0)
k, the y-coordinate, tells you the ___________________________ from (0, 0)
a tells you if the graph is further from or closer to an axis.
To graph using transformations:
1. Find the ___________________________, _________.
2. Choose some _____________ and create a ______________________________.
Ex 1
Graph y  2 x  4  1 . Move to _______
x y
5
4
3
2
1
0
1
2
3
4
5
Domain:_____________
Range:______________
Ex 2 Graph y  23 x  3  2
Move to _________
x
y
Domain:___________
Range:____________
Ex 3 Given the graph, state the function.
1. __________________ the family based on the shape.
2. Find ____________.
3. Substitute into the form and test a point to check a.
a)
b)
c)