(b)
For each input x, square it and then take its opposite. Plotting and joining the
points gives a parabola that opens down. It is a reflectionof the graph of the squaring
function across the x-axis. See the table and FIGURE 6. The domain is and the
range is
(c)
For this function, cube the input and then subtract 2 from the result. The graph
is that of the cubing function shifted2 units down. See the table and FIGURE 7. The
domain and range are both 1 - q, q 2.
ƒ 1 x 2 =x^3 - 2
1 - q, 0 4.
1 - q, q 2
ƒ 1 x 2 =-x^2
290 CHAPTER 5 Exponents, Polynomials, and Polynomial Functions
xyDomainRange(0, 0)(2, 4)
(1, 2)f(x) = 2x
(–1, –2)
(–2, – 4)FIGURE 5xy(0, 0)
DomainRange(1, –1)(2, – 4)f(x) = –x^2(–1, –1)(–2, – 4)FIGURE 6x00
12
24- 1 - 2
- 2 - 4
ƒ 1 x 2 = 2 x x00
1
2 - 4- 1
- 1 - 1
- 2 - 4
ƒ 1 x 2 =-x^2x0
1
26- 1
- 2
- 1 - 3
- 2 - 10
ƒ 1 x 2 =x^3 - 2xyDomainRange(1, –1)
(0, –2)(2, 6)
f(x) = x^3 – 2(–1, –3)(–2, –10)
FIGURE 7 NOW TRYComplete solution available
on the Video Resources on DVD
5.3 EXERCISES
For each polynomial function, find (a) and (b). See Example 1.
- 7.ƒ 1 x 2 =-x^2 + 2 x^3 - 8 8.ƒ 1 x 2 =-x^2 - x^3 + 11 x
ƒ 1 x 2 = 3 x^2 +x- 5 ƒ 1 x 2 = 5 x^4 - 3 x^2 + 6 ƒ 1 x 2 =- 4 x^4 + 2 x^2 - 1ƒ 1 x 2 = 6 x- 4 ƒ 1 x 2 =- 2 x+ 5 ƒ 1 x 2 =x^2 - 3 x+ 4ƒ 1 - 12 ƒ 122NOW TRY
EXERCISE 7
Graph. Give
the domain and range.
ƒ 1 x 2 =x^2 - 4xy(–2, 0) (^0) (2, 0)
(–3, 5) (3, 5)
(0, – 4)
f(x) = x^2 – 4
NOW TRY ANSWER
7.
domain: ;
range: 3 - 4, q 2
1 - q, q 2
Solve each problem. See Example 2.
9.Imports of Fair Trade Certified™ coffee into the United
States during the years 2000 through 2006 can be modeled by
the polynomial function defined by
where corresponds to the year 2000, corre-
sponds to 2001, and so on, and is in thousands of
pounds. Use this function to approximate the amount (to the
nearest whole number) of Fair Trade coffee imported into the
United States in each given year. (Source:TransFair USA.)
(a) 2000 (b) 2003 (c) 2006
P 1 x 2
x= 0 x= 1
P 1 x 2 = 1667 x^2 +22.78x+4300,