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Radical Functions Objectives Graph radical functions and inequalities. Transform radical functions by changing parameters. Vocabulary radical function square-root function Holt McDougal Algebra 2 Radical Functions Example 1A: Graphing Radical Functions Graph each function and identify its domain and range. x (x, f(x)) 3 4 7 12 The domain is {x|x Holt McDougal Algebra 2 }, and the range is {y| }. Radical Functions Check It Out! Example 1a Graph each function and identify its domain and range. x (x, f(x)) –8 –1 0 1 8 The domain is {x|x Holt McDougal Algebra 2 }, and the range is {y| }. Radical Functions Check It Out! Example 1a Continued Check Graph the function on a graphing calculator. Holt McDougal Algebra 2 Radical Functions Example 1B: Graphing Radical Functions Graph each function and identify its domain and range. x (x, f(x)) –6 1 2 3 10 The domain is {x|x Holt McDougal Algebra 2 }, and the range is {y| }. Radical Functions Example 1B Continued Check Graph the function on a graphing calculator. Holt McDougal Algebra 2 Radical Functions Check It Out! Example 1b Graph each function, and identify its domain and range. x (x, f(x)) –1 3 8 15 The domain is {x|x Holt McDougal Algebra 2 }, and the range is {y|y }. Radical Functions Holt McDougal Algebra 2 Radical Functions Example 2: Transforming Square-Root Functions Using the graph of f(x) = x as a guide, describe the transformation and graph the function. g(x) = x+5 Holt McDougal Algebra 2 Radical Functions Check It Out! Example 2a Using the graph of f(x)= x as a guide, describe the transformation and graph the function. g(x) = x + 1 Holt McDougal Algebra 2 Radical Functions Check It Out! Example 2b Using the graph of f(x) = x as a guide, describe the transformation and graph the function. Holt McDougal Algebra 2 Radical Functions Example 3: Applying Multiple Transformations Using the graph of f(x)= x as a guide, describe the transformation and graph the function . Holt McDougal Algebra 2 Radical Functions Example 3: Applying Multiple Transformations Using the graph of f(x)= x as a guide, describe the transformation and graph the function . Reflect f across the x-axis, and translate it 4 units to the right. Holt McDougal Algebra 2 • • Radical Functions Check It Out! Example 3a Using the graph of f(x)= x as a guide, describe the transformation and graph the function. Holt McDougal Algebra 2 Radical Functions Check It Out! Example 3a Using the graph of f(x)= x as a guide, describe the transformation and graph the function. g is f reflected across the y-axis and translated 3 units up. ● ● Holt McDougal Algebra 2 Radical Functions Check It Out! Example 3b Using the graph of f(x)= x as a guide, describe the transformation and graph the function. g(x) = –3 x – 1 Holt McDougal Algebra 2 Radical Functions Check It Out! Example 3b Using the graph of f(x)= x as a guide, describe the transformation and graph the function. g(x) = –3 x – 1 g is f vertically stretched by a factor of 3, reflected across the x-axis, and translated 1 unit down. Holt McDougal Algebra 2 ● ● Radical Functions Example 4: Writing Transformed Square-Root Functions Use the description to write the square-root function g. The parent function f(x)= x is reflected across the x-axis, compressed vertically by a factor of 1 , and translated down 5 units. 5 Holt McDougal Algebra 2 Radical Functions Check It Out! Example 4 Use the description to write the square-root function g. The parent function f(x)= x is reflected across the x-axis, stretched vertically by a factor of 2, and translated 1 unit up. Holt McDougal Algebra 2 Radical Functions Example 6: Graphing Radical Inequalities Graph the inequality . Step 1 Use the related equation y =2 x -3 to make a table of values. x y Holt McDougal Algebra 2 0 1 4 9 Radical Functions Check It Out! Example 6a Graph the inequality. Step 1 Use the related equation y = make a table of values. x y Holt McDougal Algebra 2 –4 –3 0 5 x+4 to Radical Functions Check It Out! Example 6b Graph the inequality. Step 1 Use the related equation y = make a table of values. x y Holt McDougal Algebra 2 –4 –3 0 5 3 x - 3 to Radical Functions Lesson Quiz: Part I 1. Graph the function range and domain. D:{x|x and identify its }; R:{y|y } 2. Using the graph of as a guide, describe the transformation and graph the function g(x) = -x + 3 . Holt McDougal Algebra 2