Solution Manual For Calculus Early Transcendental Functions, 8th Edition by Ron Larson, Bruce H. Edwards (Cengage Learning, 2024) ISBN: 9780357759325, All Chapters

CH AP TER 1
Preparation for Calculus

Section 1.1 Graphs and Models ............................................................................ 2

Section 1.2 Linear Models and Rates of Change ................................................. 11

Section 1.3 Functions and Their Graphs ............................................................. 22

Section 1.4 Review of Trigonometric Functions ................................................. 36

Section 1.5 Inverse Functions ............................................................................ 45

Section 1.6 Exponential and Logarithmic Functions ........................................... 62

Review Exercises ................................................................................................... 72

Problem Solving .................................................................................................... 87

,C H A P T E R 1
Preparation for Calculus
Section 1.1 Graphs and Models
1. To find the x-intercepts of the graph of an equation, 8. y  5  2x
let y be zero and solve the equation for x. To find the
x 1 0 1 2 5
3 4
y-intercepts of the graph of an equation, let x be zero 2
and solve the equation for y. y 7 5 3 1 0 1 3
2. Symmetry helps in sketching a graph because you need
only half as many points to plot. Answers will vary.

3. y   32 x  3
x-intercept: 2, 0

y-intercept: 0, 3
Matches graph (b).

4. y  9  x2 9. y  4  x2

x-intercepts: 3, 0, 3, 0 x 3 2 0 2 3

y-intercept: 0, 3 y 5 0 4 0 5
Matches graph (d).

5. y  3  x2

x-intercepts:  
3, 0 ,  3, 0 
y-intercept: 0, 3
Matches graph (a).

6. y  x3  x
10. y  x  3
2

x-intercepts: 0, 0, 1, 0, 1, 0

y-intercept: 0, 0 x 0 1 2 3 4 5 6

Matches graph (c). y 9 4 1 0 1 4 9

7. y  1x
2
2

x 4 2 0 2 4

y 0 1 2 3 4




2

, Section 1.1 Graphs and Mͅ odels 3


11. y  x  1 3
15. y 
x
x −4 −3 −2 −1 0 1 2
x 3 2 1 0 1 2 3
y 3 2 1 0 1 2 3
y 1  32 3 Undef. 3 3
2
1




12. y  x  1

x 3 2 1 0 1 2 3 1
16. y 
y 2 1 0 1 0 1 2 x  2

x 6 4 3 2 1 0 2

y  14  12 1 Undef. 1 1
2
1
4





13. y  x 6

x 0 1 4 9 16 

y 6 5 4 3 2 17. y  5 x 
 






(a) 2, y  2, 1.73 y  52  3  1.73 


14. y  x 2
 (b) x, 3  4, 3 3  5  4 
 
x 2 1 0 2 7 14 18. y  x5  5x


y 0 1 2 2 3 4





(a) 0.5, y  0.5, 2.47
(b) x, 4  1.65, 4 and x,  4  1,  4

, 4 Chapter 1 Preparation for Calculus

19. y  2 x  5
25. y  2  x
y-intercept: y  20  5  5; 0, 5 5x  1 
2 0
x-intercept: 0  2x  5 y-intercept: y   2; 0, 2
5  2x 5 0   1
2
x  52;  52 , 0 x-intercept: 0  x
5x  1

20. y  4x2  3 0  2  x
x  4; 4, 0
y-intercept: y  40  3  3; 0, 3
2



26. y  x  3x
2
x-intercept: 0  4x2  3
3x  1
2
3  4x2
None. y cannot equal 0. 02  30
y-intercept: y 
30  1
2
21. y  x2  x  2
y  0; 0, 0
y-intercept: y  02  0  2
y  2; 0,  2 x2  3x
x-intercepts: 0 
3x  1
2
x-intercepts: 0  x2  x  2
xx  3
0  x  2x  1 0 
3x  1
2

x  2, 1; 2, 0, 1, 0
x  0, 3; 0, 0, 3, 0


22. y2  x3  4x
27. x2 y  x2  4 y  0
y-intercept: y  0  40
2 3
y-intercept: 02 y  02  4 y  0
y  0; 0, 0 
 y  0; 0, 0
x-intercepts: 0  x3  4x 
x-intercept: x20  x2  40  0
0  xx  2x  2 
 x  0; 0, 0
x  0,  2; 0, 0,  2, 0

28. y  2x 
23. y  x
y-intercept: y  20  02  1
y-intercept: y  0 16  0 2
 0; 0, 0
y  1; 0, 1
x-intercepts: 0  x 16  x2
x-intercept: 0  2x  x2  1
0  x 4  x4  x 2x  x 1
2

x  0, 4,  4; 0, 0, 4, 0,  4, 0
4x2  x2  1

24. y  x  1 x2  1 3x2  1
 2 x2  1
y-intercept: y  0  1 0  1 3
y  1; 0, 1 x   3
x-intercept: 0  x  1 x2  1 3
 
3 3
x  1; 1, 0 x  ; , 0
3  3 

Note: x   3 3 is an extraneous solution.