Alg. II
Ch. 7.5 Worksheet
Name________________________
Objective: Graph square root and cube root functions.
1. Using your TI-83, graph f ( x)  x , and sketch at right.
A. At what point does the graph begin?
(
, )
B. What is the domain of the graph?
D: ______________
C. What is the range of the graph?
R: ______________
2. Now enter f ( x)  x  3 , and sketch.
A. At what point does this graph begin?
(
, )
B. What is the domain of the graph?
D: ______________
C. What is the range of the graph?
R: ______________
D. How was the parent function of f ( x)  x transformed?
3. Now graph and sketch y  x  2 .
A. At what point does the graph begin?
(
, )
B. What is the domain of the graph?
D: ______________
C. What is the range of the graph?
R: ______________
D. How was the parent function of f ( x)  x transformed?
4. How do you think the parent function of f ( x)  x will be transformed (moved) by
changing it to f ( x)  x  4  2 ?
5. Check to see if you were correct by graphing f ( x)  x  4  2 . Were you correct?
6. Using your TI-83, graph f ( x)  3 x , then sketch it on the x-y coordinate plane.
A. What is the domain of this graph?
D: ______________
B. What is the range of the graph?
R: ______________
7. Without erasing #6, graph f ( x)  3 x  2 ,
And then sketch it on the x-y plane at right.
A. How does this graph compare to the
graph from #6?
B. What is the domain of the graph?
D: ______________
C. What is the range of the graph?
R: ______________
8. Now graph and sketch y  3 x  1 .
A. What is the domain of the graph?
D: ______________
B. What is the range of the graph?
R: ______________
D. How was the parent function of f ( x)  3 x transformed?
9. How do you think the parent function of f ( x)  3 x will be transformed (moved) by
changing it to f ( x)  3 x  3.5  2.7 ? Graph it on your TI-83 to see if you are right.
10. Clear your TI-83. Graph y   x by graphing both y  x and y   x . Sketch
the two graphs below. Putting the two together, what shape is formed?
11. What is the domain of this graph?
12. Adding to the two graphs in #10, graph and
sketch y  x 2 . What shape is this?
13. Add to your graphs by entering the line y  x .
Sketch this line on the graph at right. Is this the
line of symmetry?
Generic Formula: y  n x  h  k moves the parent function h units right or left,
and k units up or down.