C6L8 Notes
Graphs of Square Root and Cube Root Functions
Rigid transformations
*
*
*
*
*
*
vertical shift c units up:
vertical shift c units down:
horizontal shift c units right:
horizontal shift c units left:
reflection on the x-axis:
reflection on the y-axis:
Non-rigid transformations
* vertical stretch
* horizontal stretch
h(x) = f(x) + c
h(x) = f(x) – c
h(x) = f(x – c)
h(x) = f(x + c)
h(x) = -f(x)
h(x) = f(-x)
y = c f(x)
c>1
0<c<1
Parent Functions:
Square Root
Cube Root
y
y
x
x
Graph each equation. State the domain, range, and intercepts.
2. = √ +
1. = √ −
y
y
x
x
Domain: ____________________
Domain: _____________________
Range: _____________________
Range: _______________________
x-int: _______ y-int: _______
x-int: _______ y-int: _______
3. = √ −
4. = √ +
y
y
x
x
Domain: ____________________
Domain: _____________________
Range: _____________________
Range: _______________________
x-int: _______ y-int: _______
x-int: _______ y-int: _______
5. = −√
6. = √ − +
y
y
x
x
Domain: ____________________
Domain: _____________________
Range: _____________________
Range: _______________________
x-int: _______ y-int: _______
x-int: _______ y-int: _______
7. = −√ + +
8. = √ − −
y
y
x
x
Domain: ____________________
Domain: _____________________
Range: _____________________
Range: _______________________
x-int: _______ y-int: _______
x-int: _______ y-int: _______
9. = . √ + −
10. = −. √ + −
y
y
x
x
Domain: ____________________
Domain: _____________________
Range: _____________________
Range: _______________________
x-int: _______ y-int: _______
x-int: _______ y-int: _______
11. = √ −
12. = √ +
y
y
x
x
Domain: ____________________
Domain: _____________________
Range: _____________________
Range: _______________________
x-int: _______ y-int: _______
x-int: _______ y-int: _______
13. = √ −
14. = √ +
y
y
x
x
Domain: ____________________
Domain: _____________________
Range: _____________________
Range: _______________________
x-int: _______ y-int: _______
x-int: _______ y-int: _______
15. = √ + −
16. = √ − +
y
y
x
x
Domain: ____________________
Domain: _____________________
Range: _____________________
Range: _______________________
x-int: _______ y-int: _______
x-int: _______ y-int: _______
17. You can model the population of a certain city between the years
1955 and 2005 by the radical function = √ − . Using
this model, in what year was the population of that city _____________?