Parent Function Worksheet 1

Name ____________________________ Date ______________ Period _______
U2 – S1 – L5 Transformations of Functions: Use Desmos
# 1- 7
Identify the type of function, the Parent Function, and describe the transformation represented.
1. g(x) = x 2 – 1
Type: ________________________________Parent Function: __________________
Transformation:________________________________
2. f(x) = 2 x 1
Type: ________________________________Parent Function: __________________
Transformation:________________________________
x2
Type: ________________________________Parent Function: __________________
Transformation:________________________________
3. h(x) =
4. g(x) = x3+ 3
Type: ________________________________Parent Function: __________________
Transformation:________________________________
5. g(x) = x  6
Type: ________________________________Parent Function: __________________
Transformation:________________________________
6. f(x) = x  5 - 2
Type: ________________________________Parent Function: __________________
Transformation:________________________________
7. h(x) =
1 2
x 5
2
Type: ________________________________Parent Function: __________________
Transformation:________________________________
#8-12 Identify the domain and range of the function in set & interval notation. Describe the
transformation from its parent function.
8. g(x) = 3 x
Domain : _____________________ Range : ___________________
Transformation:_____________________________________________
9. h(x) = - x2 + 1
Domain : _____________________ Range : ___________________
Transformation:_____________________________________________
10. h(x) =  x  2
Domain : _____________________ Range : ___________________
Transformation:_____________________________________________
11. f(x) =
3 3
x
4
Domain : _____________________ Range : ___________________
Transformation:_____________________________________________
12. h(x) = x+9
Domain : _____________________ Range : ___________________
Transformation:_____________________________________________
#13 - 17 Given the parent function and a description of the transformation, write the equation of the
transformed function, f(x).
13. Absolute value—vertical shift up 5, horizontal shift right 3.
____________________
14. Square Roots —Two units left, seven units up
____________________
15. Cubic—decreases and vertical shift down 2
____________________
16. Absolute value – expanded “v” shape, 3 right, 1 down
____________________
17. Quadratic—contracted, horizontal shift left 8.
____________________
18. Which graph best represents the function f(x) = 2x2 - 2?
a.
b.
c.
________________
d.
19. Name the six parent functions that we are studying.
______________________
_____________________
___________________
______________________
_____________________
___________________
20. Create a transformation and describe how it is translated from the parent function.
a)
Linear – ____________________________________
Transformation: ______________________________________
b) Absolute Value - ____________________________________
Transformation: ______________________________________
c)
Quadratic - ______________________________________
Transformation: ______________________________________
d) Cubic - _____________________________________
Transformation: ______________________________________
e)
Square Root - _____________________________________________
Transformation: ______________________________________