Intermediate Algebra (11th edition)

FIGURE 2shows the graph of the cube root function.Since any real number (pos-

itive, negative, or 0) can be used for xin the cube root function, can be positive,

negative, or 0. Thus, both the domain and the range of the cube root function are

1 - q, q 2.

23 x

430 CHAPTER 8 Roots, Radicals, and Root Functions

2

1

x

x

• 8


• 1
  0
  1
  8
  
  
  • 2
  
  
  • 1
    0
    1
    2
    18
  
  
  
  

y

• 2


• 8

f (x)^3 x

f (x)^3 x

FIGURE 2

Cube root function

Domain:

Range: 1 - q, q 2

1 - q, q 2

ƒ 1 x 2  23 x

Graphing Functions Defined with Radicals

Graph each function by creating a table of values. Give the domain and range.

(a)

A table of values is given with the graph in FIGURE 3. The x-values were chosen in

such a way that the function values are all integers. For the radicand to be nonnega-

tive, we must have

or

Therefore, the domain of this function is Function values are positive or 0, so

the range is 3 0, q 2.

3 3, q 2.

x- 3 Ú0, xÚ 3.

ƒ 1 x 2 = 2 x- 3

EXAMPLE 3

x

y

0

1

2

34 7

f(x) = √x – 3

FIGURE 3

x

y

f(x) = √^3 x + 2

–1 1

1

2

4

–8 8

FIGURE 4

x

3

4

7 27 - 3 = 2

24 - 3 = 1

23 - 3 = 0

ƒ 1 x 2 = 2 x- 3

x

0

1

8 238 + 2 = 4

231 + 2 = 3

230 + 2 = 2

• 1 23 - 1 + 2 = 1


• 8 23 - 8 + 2 = 0

ƒ 1 x 2 = 23 x+ 2

(b)

See FIGURE 4. Both the domain and range are 1 - q, q 2.

ƒ 1 x 2 = 23 x+ 2

NOW TRY

NOW TRY
EXERCISE 3
Graph each function. Give the
domain and range.

(a)

(b)ƒ 1 x 2 = 23 x- 1

ƒ 1 x 2 = 2 x+ 1

NOW TRY ANSWERS

3. (a)

domain: ;

range:

(b)

domain: ;

range: 1 - q, q 2

1 - q, q 2

0

y

x

–1 1

–2

f(x) = ^3 x – 1

3 0, q 2

3 - 1, q 2

2

0

y

x

–1 3

f(x) = x + 1