1. Chapter 6 Radical Functions and Rational Exponents

2. 6-8 Graphing Radical Functions What you’ll learn … Graph radical functions

3. A radical equation defines a radical function. The graph of the radical function y= √x + k is a translation of the graph of y= √x. If k is positive, the graph is translated k units up. If k is negative, the graph is translated k units down.

4. Example 1 Translating Square Root Functions Vertically y = √xy = √x + 3

5. Example 2 Translating Square Root Functions Horizontally y = √xy = √x + 3

6. Example 3 Graphing Square Root Functions y = -√x

7. Example 4 Graphing Square Root Functions y = -2√x+1 - 3

8. Real World Connection The function h(x) = 0.4 √ x models the height h in meters of a female giraffe that has a mass of x kilograms. Graph the model with a graphing calculator. Use the graph to estimate the mass of the young giraffe in the photo. 3 2.5 m

9. Example 6 Graphing Cube Root Functions y = 2√x+3 - 1 3

10. Example 7 Transforming Radical Equations Rewrite to make it easy to graph using a translation. Describe the graph. y = √4x-12 Rewrite to make it easy to graph using a translation. Describe the graph. y = √8x-24 +3 3

11. In this chapter, you should have … Extended your knowledge of roots to include cube roots, fourth roots, fifth roots, and so on. Learned to add, subtract, multiply, and divide radical expressions, including binomial radical expressions. Solved radical equations, and graphed translations of radical functions and their inverses.