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