19,25 12. True or False If the degree of the numerator of a rationalfunction equals the degree of the denominator, then thedivided by x – x² + 1. (pp. A25-11. If a rational function is proper, thenasymptote.is a horizontalConcepts and Vocabulary5. True or False The domain of every rational function is theset of all real numbers.6. If, as x→- 00 or as x- 00, the values of R(x)approach some fixed number L, then the line y = L is aof the graph of R.rational function has a horizontal asymptote.P(x)is a rational function and9 (x)7. If, as x approaches some number c, the valuesof |R(x)|→0, then the line x = c is a13. Multiple Choice If R(x) =if p and q have no common factors, then Ris(b) proper(d) in lowest termsof the graph of R.(a) improper(c) undefined14. Multiple Choice Which type of asymptote, when it oOdescribes the behavior of a graph when x is close to cnumber?8. For a rational function R, if the degree of the numerator isless than the degree of the denominator, then R is9. True or False The graph of a rational function may intersecta horizontal asymptote.10. True or False The graph of a rational function may intersecta vertical asymptote.(a) vertical (b) horizontal (c) oblique (d) all of theseSkill BuildingIn Problems 15-26, find the domain of each rational function.4x5x216. R(x) =-4x215. R(x)17. H(x)x - 73 + x(x – 2) (x + 4)3x (x - 1)2x – 5x – 126.18. G(x)-x(1 – x)3x2 + 5x – 2(x + 3) (4 – x)19. F(x) =20. Q(x)21. R(x) =22. R(x) =3x + xx2 + 9x - 64x* - 123. H(х) —x - 324. G(x) =3(x - x - 6)5(x - 4)x* + 125. R(x)-2(x – 4)3(x² + 4x + 4)26. F(x)In Problems 27–32, use the graph shown to find(a) The domain and range of each function(d) Vertical asymptotes, if any(b) The intercepts, if any(e) Oblique asymptotes, if any27.(c) Horizontal asymptotes, if any28.29.(0, 2)13(1, 2),(-1, 0)(1, 0)3 x

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Description: 19,25 12. True or False If the degree of the numerator of a rationalfunction equals the degree of the denominator, then thedivided by x – x² + 1. (pp. A25-11. If a rational function is proper, thenasymptote.is a horizontalConcepts and Vocabulary5. Tr

The domain of any function consists of all real numbers except the values of x for which the…

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Calculus

In Problems 15–26, find the domain of each rational function. 5x 3+ x -4x2 \ 17. H(x) 4x 16. R(x) (x – 2) (x + 4) %3D 15. R(x) x - 7 3x(x- 1) 21 - 5x - 12 -x(1 - x) 3x + 5x - 2 18. G(x) : 6. 19. F(x) 20. Q(x) = %3D %3D (x + 3) (4 – x) | 3x + x 21. R(x) 22. R(x) 23. H (х) %3D * - 64 x² + 9 3(x-x-6) 5(x - 4) 24. G(x) x - 3 %3D 25. R(x) 26. F(x) -2(x - 4) %3D x* + 1 %3D

In Problems 15–26, find the domain of each rational function. 5x 3+ x -4x2 \ 17. H(x) 4x 16. R(x) (x – 2) (x + 4) %3D 15. R(x) x - 7 3x(x- 1) 21 - 5x - 12 -x(1 - x) 3x + 5x - 2 18. G(x) : 6. 19. F(x) 20. Q(x) = %3D %3D (x + 3) (4 – x) | 3x + x 21. R(x) 22. R(x) 23. H (х) %3D * - 64 x² + 9 3(x-x-6) 5(x - 4) 24. G(x) x - 3 %3D 25. R(x) 26. F(x) -2(x - 4) %3D x* + 1 %3D

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

19,25

12. True or False If the degree of the numerator of a rational
function equals the degree of the denominator, then the
divided by x – x² + 1. (pp. A25-
11. If a rational function is proper, then
asymptote.
is a horizontal
Concepts and Vocabulary
5. True or False The domain of every rational function is the
set of all real numbers.
6. If, as x→- 00 or as x- 00, the values of R(x)
approach some fixed number L, then the line y = L is a
of the graph of R.
rational function has a horizontal asymptote.
P(x)
is a rational function and
9 (x)
7. If, as x approaches some number c, the values
of |R(x)|→0, then the line x = c is a
13. Multiple Choice If R(x) =
if p and q have no common factors, then Ris
(b) proper
(d) in lowest terms
of the graph of R.
(a) improper
(c) undefined
14. Multiple Choice Which type of asymptote, when it oO
describes the behavior of a graph when x is close to c
number?
8. For a rational function R, if the degree of the numerator is
less than the degree of the denominator, then R is
9. True or False The graph of a rational function may intersect
a horizontal asymptote.
10. True or False The graph of a rational function may intersect
a vertical asymptote.
(a) vertical (b) horizontal (c) oblique (d) all of these
Skill Building
In Problems 15-26, find the domain of each rational function.
4x
5x2
16. R(x) =
-4x2
15. R(x)
17. H(x)
x - 7
3 + x
(x – 2) (x + 4)
3x (x - 1)
2x – 5x – 12
6.
18. G(x)
-x(1 – x)
3x2 + 5x – 2
(x + 3) (4 – x)
19. F(x) =
20. Q(x)
21. R(x) =
22. R(x) =
3x + x
x2 + 9
x - 64
x* - 1
23. H(х) —
x - 3
24. G(x) =
3(x - x - 6)
5(x - 4)
x* + 1
25. R(x)
-2(x – 4)
3(x² + 4x + 4)
26. F(x)
In Problems 27–32, use the graph shown to find
(a) The domain and range of each function
(d) Vertical asymptotes, if any
(b) The intercepts, if any
(e) Oblique asymptotes, if any
27.
(c) Horizontal asymptotes, if any
28.
29.
(0, 2)
13
(1, 2),
(-1, 0)
(1, 0)
3 x

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