SQUARE ROOT Functions Radical functions 11252020 11 28

SQUARE ROOT Functions Radical functions 11/25/2020 11: 28 PM 8 -7: Square Root Graphs 1

REVIEW A radical function is a function whose rule is a radical expression, which include the squareroot function, 11/25/2020 11: 28 PM 8 -7: Square Root Graphs 2

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EXAMPLE 1 Graph each function and identify its domain and range of x Domain: 11/25/2020 11: 28 PM f(x) g(x) Range: 8 -7: Square Root Graphs 4

EXAMPLE 2 Graph each function and identify its domain and range of Domain: 11/25/2020 11: 28 PM Range: 8 -7: Square Root Graphs 5

EXAMPLE 3 Using the graph, f(x) = , as a guide, describe the transformation, identify the domain and range, and graph the function, Domain: g(x) Range: g(x) translates 4 units right 11/25/2020 11: 28 PM 8 -7: Square Root Graphs 6

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) translates 4 units down 11/25/2020 11: 28 PM 8 -7: Square Root Graphs 7

YOUR TURN Using the parent function as a guide, describe the transformation, identify the domain and range, and graph the function, Range: Domain: g(x) translates 5 units left and 5 units down 11/25/2020 11: 28 PM 8 -7: Square Root Graphs 8

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 11/25/2020 11: 28 PM 8 -7: Square Root Graphs 9

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. • •

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

Check It Out! Example 3 b 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. ● ●

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 5 , and translated down 5 units.

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.

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 0 1 4 9

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 yaxis.

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

Check It Out! Example 6 a Graph the inequality. Step 1 Use the related equation y = make a table of values. x y – 4 0 – 3 1 0 2 5 3 x+4 to

Check It Out! Example 6 a 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 less than – 4, do not shade left of – 4.

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

Check It Out! Example 6 b Graph the inequality. Step 1 Use the related equation y = make a table of values. x y – 4 0 – 3 1 0 2 5 3 3 x - 3 to

Check It Out! Example 6 b 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.

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

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

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

Lesson Quiz: Part III 3. Graph the inequality .

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