Holt Algebra 2

8-7 Radical Functions

Warm Up

Identify the domain and range of each function.

D: R; R:{y|y ≥2}1. f(x) = x2 + 2

D: R; R: R2. f(x) = 3x3

Use the description to write the quadratic function g based on the parent function f(x) = x2.

3. f is translated 3 units up. g(x) = x2 + 3

g(x) =(x + 2)24. f is translated 2 units left.

Holt Algebra 2

8-7 Radical Functions

• Graph radical functions• Transform radical functions by

changing parameters.

Objectives

Holt Algebra 2

8-7 Radical Functions

Make a table of values. Plot enough ordered pairs to see the shape of the curve. Choose both negative and positive values for x if possible.

Check It Out! Example 1

Holt Algebra 2

8-7 Radical Functions

x (x, f(x))

–1 0

1

4

9

Holt Algebra 2

8-7 Radical Functions

Holt Algebra 2

8-7 Radical Functions

Make a table of values. Plot enough ordered pairs to see the shape of the curve. Choose both negative and positive values for x if possible.

Check It Out! Example 2

Holt Algebra 2

8-7 Radical Functions

x (x, f(x))–8 (–8, –2)

–1 (–1,–1)

0 (0, 0)

1 (1, 1)

8 (8, 2)

•

• •

• •

The domain is the set of all real numbers. The range is also the set of all real numbers.

Check It Out! Example 2 Continued

Holt Algebra 2

8-7 Radical Functions

x (x, f(x))

–1

3

8

15

Check It Out! Example 3

Graph each function, and identify its domain and range.

Holt Algebra 2

8-7 Radical Functions

x (x, f(x))–1 (–1, 0)

3 (3, 2)

8 (8, 3)

15 (15, 4)

The domain is {x|x ≥ –1}, and the range is {y|y ≥0}.

•

••

•

Check It Out! Example 3

Graph each function, and identify its domain and range.

Holt Algebra 2

8-7 Radical Functions

The graphs of radical functions can be transformed by using methods similar to those used to transform linear, quadratic, polynomial, and exponential functions. This lesson will focus on transformations of square-root functions.

Holt Algebra 2

8-7 Radical Functions

Holt Algebra 2

8-7 Radical Functions

Using the graph of as a guide, describe the transformation and graph the function.

Translate f 1 unit up. ••

Check It Out! Example 4

g(x) = x + 1

f(x)= x

Holt Algebra 2

8-7 Radical Functions

Using the graph of as a guide, describe the transformation and graph the function.

Check It Out! Example 5

g is f vertically compressed

by a factor of .1

2

f(x) = x

Holt Algebra 2

8-7 Radical Functions

General Equation

The general form of the square root function is

y a x h k The cube root function is

3y a x h k

Holt Algebra 2

8-7 Radical Functions

g is f vertically stretched by a factor of 3, reflected across the x-axis, and translated 1 unit down.

●●

Try these!

Using the graph of as a guide, describe the transformation and graph the function.

f(x)= x

g(x) = –3 x – 1

Holt Algebra 2

8-7 Radical Functions

Use the description to write the square-root function g.

Check It Out! Example 6

The parent function is reflected across the x-axis, stretched vertically by a factor of 2, and translated 1 unit up.

f(x)= x

Holt Algebra 2

8-7 Radical Functions

Use the description to write the square-root function g.

Check It Out! Example 6 Solution

The parent function is reflected across the x-axis, stretched vertically by a factor of 2, and translated 1 unit up.

Step 1 Identify how each transformation affects the function.

Reflection across the x-axis: a is negative

Translation 1 unit up: k = 1

Vertical compression by a factor of 2 a = –2

f(x)= x

Holt Algebra 2

8-7 Radical Functions

Simplify.

Substitute –2 for a and 1 for k.

Step 2 Write the transformed function.

Check Graph both functions on a graphing calculator. The g indicates the given transformations of f.

Check It Out! Example 6 Continued