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Graphing Radical Functions for Translations

Learn how to graph radical functions and equations by translating them vertically and horizontally. Explore examples and real-world applications of square root and cube root functions.

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Graphing Radical Functions for Translations

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  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 = √x y = √x+ 3

  5. Example 2 Translating Square Root Functions Horizontally y = √x y = √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 3 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. 2.5 m

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

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

  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.

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