Graphing Radical Functions
Exploration Guide
The Graph of the Square Root Function
In this section, you will experiment with changing the values of h and k in
y
x  h  k . On the Controls tab, with a = 1.0, h = 0.0, and k = 0.0, click on
y a x h k.
1. What is the equation in the red box? _________________________________
2. Click on the Table tab; change the min to 0 and the max to 9. Fill in the t-chart
with the points on the curve. Sketch the graph using the points in the t-chart.
This is the parent function for all square root functions.
Click on the Controls tab and vary h by moving the h slider.
3. What is the effect on the graph as h increases?________________________
4. What is the effect on the graph as h decreases?________________________
5. Set h = 3.0. What is the equation in the red box? ________________________
6. How did this change the parent graph? _________________________________
7. Click on the Table tab and fill in the t-chart with the points on the curve. Sketch
the graph using those points.
8. How do the x-values in the table compare to the x-values in the parent function’s
table? ___________________________________________________________
Go back to the Controls tab and set h = 0.0. Vary k by moving the k slider.
9. What is the effect on the graph as k increases? ________________________
10. What is the effect on the graph as k decreases? _______________________
11. Set the value of k to 2.0 . What is the equation in the red box? ______________
12. How did this change the parent graph? _________________________________
13. Click on the Table tab and fill in the t-chart with the points on the curve. Sketch
the graph using those points.
14. How do the y-values in the table compare to the y-values in the parent function’s
graph? _________________________________________________________
Go back to the Controls tab and set h = 0.0 and k = 0.0. Vary the value of a by
moving the a slider.
15. When a is positive, is the graph increasing or decreasing? ________________
16. When a is negative, is the graph increasing or decreasing? ________________
17. As the absolute value of a increases, does the graph become more or less
steep?___________________________________________________________
18. Change the value of a to 2. What is the equation in the red box? ____________
19. How did this change the parent graph? _________________________________
20. Click on the Table tab and fill in the t-chart with the points on the curve. Sketch
the graph using those points.
21. How do the y-values in the table compare to the y-values in the parent function’s
table?
Change the values to make a  0.5, h  3, and k  1.
22. What is the equation in the red box?___________________________________
23. How will the graph change? __________________________________________
24. Click on the Table tab and fill in the t-chart with the points on the curve. Sketch
the graph using those points.
The Graph of the Cube Root Function
In this section, you will explore the graph of y  a 3 x  h  k . On the Controls tab,
select the cube root function. Set a = 1.0, h = 0.0, and k = 0.0, click on
y  a3 x  h  k .
1. What is the equation in the red box? ___________________________________
2. Click on the Table tab and fill in the t-chart with the points on the curve. (It might
be helpful to change the min to 10 and the max to 10.) Sketch the graph using
the points in the t-chart. This is the parent function for all cube root functions.
Click on the Controls tab and vary h by moving the h slider.
3. How does the graph change when you increase the value of h? _____________
4. How does the graph change when you decrease h? _______________________
5. Set h = 2.0 . What is the equation in the red box? ________________________
6. How did this change the parent graph? _________________________________
7. Click on the Table tab and fill in the t-chart with the points on the curve. Sketch
the graph using those points.
8. How do the x-values in the table compare to the x- values in the parent function’s
table? ___________________________________________________________
Go back to the Controls tab and set h = 0.0. Vary k by moving the k slider.
9. What is the effect on the graph as k increases? __________________________
10. What is the effect on the graph as k decreases? _________________________
11. Set the value of k to 5. What is the equation in the red box? _________________
12. How did this change the parent graph? _________________________________
13. Click on the Table tab and fill in the t-chart with the points on the curve. Sketch
the graph using those points.
14. How do the x-values in the table compare to the x-values in the parent function’s
table?__________________________________________________________
Go back to the Controls tab and set h = 0.0 and k = 0.0. Vary the value of a by
moving the a slider.
15. As the absolute value of a increases, does the graph become more or less
steep? ________________________________________________________
16. When a is positive, is the graph increasing or decreasing from left to right?
______________________________________________________________
17. When a is negative, is the graph increasing or decreasing from left to right?
______________________________________________________________
18. Change the value of a to 1. What is the equation in the red box? ____________
19. How did this change the parent graph? _________________________________
20. Click on the Table tab and fill in the t-chart with the points on the curve. Sketch
the graph using those points.
21. How do the y-values in the table compare to the y-values in the parent function’s
table? _________________________________________________________
Change the values to make a  0.5, h  1, and k  4 .
22. What is the equation in the red box? __________________________________
23. How will these values change the graph? _______________________________
24. Click on the Table tab and fill in the t-chart with the points on the curve. Sketch
the graph using those points.
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