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Section 7-8

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**1. **Section 7-8 Graphing Square Root and Other Radical Functions

**2. **Quadratic and its Inverse

**3. **Restrict the Domain We can restrict the domain on the graph of f(x) = x2 so that its inverse is a function.

**4. **Cubic and its Inverse

**5. **The inverse function of y = x², y=vx, with a restricted domain is the parent function for the family of square root functions.
The inverse function of y = xn, , with a restricted domain is the parent function for the family of radical functions.

**6. **Fill out the table below using

**8. **This is the parent function for the square root function.
We will do the same transformations as we did with the absolute value parent function and the quadratic parent function.

**9. **Families of Radical Functions

**10. **Ex: Graphing Square Root Functions Graph the parent function of the square root function and the following function on the same graph. Tell what transformation were done to the square root parent function. Graph at least four points on each.

**13. **Graph the parent function of the square root function and the following function on the same graph. Tell what transformation were done to the square root parent function. Graph at least three points on each.

**16. **Graph the parent function of the square root function and the following function on the same graph. Tell what transformation were done to the square root parent function. Graph at least four points on each.

**19. **Graph the parent function of the square root function and the following function on the same graph. Tell what transformation were done to the square root parent function. Graph at least four points on each.

**22. **Graph the parent function of the square root function and the following function on the same graph. Tell what transformation were done to the square root parent function. Graph at least three points on each.

**24. **Graph the parent function of the square root function and the following function on the same graph. Tell what transformation were done to the square root parent function. Graph at least three points on each.

**27. **Graph the parent function of the square root function and the following function on the same graph. Tell what transformation were done to the square root parent function. Graph at least three points on each.

**29. **Graph the parent function of the cube root function and the following function on the same graph. Tell what transformation were done to the cube root parent function. Graph at least three points on each.
a.

**32. **Graph the parent function of the cube root function and the following function on the same graph. Tell what transformation were done to the cube root parent function. Graph at least three points on each.
b.

**34. **Graph the parent function of the cube root function and the following function on the same graph. Tell what transformation were done to the cube root parent function. Graph at least three points on each.
c.

**36. **Rewriting Radical Functions Sometimes you have to rewrite a radical function so you can graph it using transformations.
Rewrite to make it easy to graph using transformations. Describe the graph.

**37. **Rewriting Radical Functions
Rewrite to make it easy to graph using transformations. Describe the graph.

**38. **Solve Square Root Equations by Graphing The speed v of an object in meters per second can be modeled by
where KE is its kinetic energy in Joules and m its mass in kilograms. Find the kinetic energy for a 70 kilogram bicycle and rider traveling at a speed of 10 meters per second.