10/11/ :27 AM8-7: Square Root Graphs1 SQUARE ROOT Functions Radical functions

10/11/ :27 AM8-7: Square Root Graphs2 REVIEW A radical function is a function whose rule is a radical expression, which include the square- root function,

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10/11/ :27 AM8-7: Square Root Graphs4 EXAMPLE 1 Graph each function and identify its domain and range of Domain: Range: g(x)g(x) xf(x)f(x)

10/11/ :27 AM8-7: Square Root Graphs5 EXAMPLE 2 Graph each function and identify its domain and range of Domain: Range:

10/11/ :27 AM8-7: Square Root Graphs6 EXAMPLE 3 Using the graph, f(x) =, as a guide, describe the transformation, identify the domain and range, and graph the function, Domain: Range: g(x)g(x) g(x) translates 4 units right

10/11/ :27 AM8-7: Square Root Graphs7 EXAMPLE 4 Using the parent function as a guide, describe the transformation, identify the domain and range, and graph the function, Domain: Range: g(x)g(x) g(x) translates 4 units down

10/11/ :27 AM8-7: Square Root Graphs8 YOUR TURN Using the parent function as a guide, describe the transformation, identify the domain and range, and graph the function, Domain: Range: g(x)g(x) g(x) translates 5 units left and 5 units down

10/11/ :27 AM8-7: Square Root Graphs9 YOUR TURN Graph each function and identify its domain and range of Domain: Range: g(x) translates 1 unit right, 3 units up and stretches by a factor of 2

Example 3: Applying Multiple Transformations Reflect f across the x-axis, and translate it 4 units to the right. Using the graph of as a guide, describe the transformation and graph the function. f(x)= x

Lesson Quiz: Part II g is f reflected across the y-axis and translated 3 units up. Using the graph of as a guide, describe the transformation and graph the function. g  x  = x + 3

g is f vertically stretched by a factor of 3, reflected across the x-axis, and translated 1 unit down. ● ● Check It Out! Example 3b Using the graph of as a guide, describe the transformation and graph the function. f(x)= x g(x) = –3 x – 1

Example 4: Writing Transformed Square-Root Functions Use the description to write the square-root function g. The parent function is reflected across the x-axis, compressed vertically by a factor of, and translated down 5 units. 1 5 f(x)= x

Use the description to write the square-root function g. Check It Out! Example 4 The parent function is reflected across the x-axis, stretched vertically by a factor of 2, and translated 1 unit up. f(x)= x

Example 6: Graphing Radical Inequalities x0149 y Graph the inequality. Step 1 Use the related equation to make a table of values. y =2 x 3

Example 6 Continued Step 2 Use the table to graph the boundary curve. The inequality sign is >, so use a dashed curve and shade the area above it. Because the value of x cannot be negative, do not shade left of the y-axis.

Example 6 Continued Check Choose a point in the solution region, such as (1, 0), and test it in the inequality. 0 > 2(1) – 3 0 > –1

Graph the inequality. x–4–305 y0123 Check It Out! Example 6a Step 1 Use the related equation to make a table of values. y = x+4

Step 2 Use the table to graph the boundary curve. The inequality sign is >, so use a dashed curve and shade the area above it. Because the value of x cannot be less than –4, do not shade left of –4. Check It Out! Example 6a Continued

Check Choose a point in the solution region, such as (0, 4), and test it in the inequality. 4 > (0) > 2 Check It Out! Example 6a Continued

Graph the inequality. x–4–305 y0123 Check It Out! Example 6b Step 1 Use the related equation to make a table of values. 3 y  x  3

Step 2 Use the table to graph the boundary curve. The inequality sign is >, so use a dashed curve and shade the area above it. Check It Out! Example 6b Continued

Check Choose a point in the solution region, such as (4, 2), and test it in the inequality. 2 ≥ 1 Check It Out! Example 6b Continued

Lesson Quiz: Part I D:{x|x≥ –4}; R:{y|y≥ 0} 1. Graph the function and identify its range and domain.

Lesson Quiz: Part II g is f reflected across the y-axis and translated 3 units up. 2. Using the graph of as a guide, describe the transformation and graph the function. g  x  = x + 3

Lesson Quiz: Part III 3. Graph the inequality.

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