Advanced Algebra Notes
Section 6.5: Graphing Square Root and Cubic Root Functions
The graphs of
y x
and
y3 x
radical functions
are examples_____________________.
In this lesson we will learn how to graph functions of the form y  a x  h  k and
y  a xh k .
a : is a vertical compression or expansion
h: shifts the graph horizontally rt./lt.
k: shifts the graph vertically up/down.
Steps:
Multiply the y-coordinate from the parent function by the a-value.
1. ______________________________________________________
Shift the x –coordinate from the parent function h units horizontally (Rt. Or LT.)
2. ______________________________________________________
Shift the y-coordinate from step 1, k units vertically (Up or Down).
3. ______________________________________________________
3
Examples:
1. y  2 x  4  1
Parent Function:
𝑥
0
1
4
9
𝑦
0
1
2
3
𝑦=
𝑥
𝑥
0
1
4
9
𝑦
0
2
4
6
𝑥
−4
−3
0
5
𝑦
−1
1
3
5
2.
y
53
x2 3
2
Parent Function:
𝑦=
3
𝑥
𝑥 𝑦
−8 − 2
−1 − 1
0 0
1 1
8 2
𝑥 𝑦
−8 5
5
−1
2
0 0
1
8
5
2
−5
−
𝑦
𝑥
8
−6
5.5
1
3
2
0.5
3
10 − 2
Example 3:
State the domain and range of the function in Example 1 and Example 2.
1.
y  2 x  4 1
Domain -
Range -
2.
x > -4
y > -1
53
y
x2 3
2
Domain –
Range -
All Real Numbers
All Real Numbers