Intermediate Algebra (11th edition)

(Marvins-Underground-K-12) #1

NOTE A linear function(Section 3.6)is a specific kind of polynomial function.


SECTION 5.3 Polynomial Functions, Graphs, and Composition 289



  • 2

  • 1
    0
    1
    2

    • 2

    • 1
      0
      1
      2




x


(0, 0) x

y

f f (x) x f f (x) x


(1, 1)

(2, 2)

(–1, –1)
(–2, –2)

FIGURE 2

Identity function

Domain:
Range: 1 - q, q 2

1 - q, q 2

ƒ 1 x 2 x

Another polynomial function, defined by and graphed in FIGURE 3, is


the squaring function.For this function, every real number is paired with its square.


The graph of the squaring function is a parabola.


ƒ 1 x 2 x^2



  • 2

  • 1
    0
    1
    2


4
1
0
1
4

x


(0, 0) x

y

f f (x) x^2 f f (x) x^2


(–1, 1) (1, 1)


(–2, 4) (2, 4)


FIGURE 3

Squaring function

Domain:
Range: 3 0, q 2

1 - q, q 2

ƒ 1 x 2 x^2

The cubing functionis defined by and graphed in FIGURE 4. This


function pairs every real number with its cube.


ƒ 1 x 2 x^3


(–2, –8)


x

y

f (x) x^3



  • 2

  • 1
    0
    1
    2

    • 8

    • 1
      0
      1
      8




x


(0, 0)

(1, 1)
(–1, –1)

(2, 8)

f (x) x^3



  • 2


2

6

4

FIGURE 4

Cubing function

Domain:
Range: 1 - q, q 2

1 - q, q 2

ƒ 1 x 2 x^3

Graphing Variations of Polynomial Functions

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


of each function by observing its graph.


(a)


To find each range value, multiply the domain value by 2. Plot the points and join


them with a straight line. See FIGURE 5on the next page. Both the domain and the


range are 1 - q, q 2.


ƒ 1 x 2 = 2 x


EXAMPLE 7

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