Solution Manual For Calculus 12th Edition by Ron Larson (Author), Bruce H. Edwards (Author)

© 2023 Cengage Learning. All Rights Reserved. May not be scanned, copi ed or duplicated, or posted to a publicly accessible webs ite, in whole or in part. CHAPTER P Preparation for Calculus Section P.1 Graphs and Models ................................................................................. 2 Section P.2 Linear Models and Rates of Change .................................................... 11 Section P.3 Functions and Their Graphs ................................................................. 22 Section P.4 Review of Trigono metric Functions .................................................... 35 Review Exercises .......................................................................................................... 44 Problem Solving ........................................................................................................... 55 2 © 2023 Cengage Learning. All Rights Reserved. May not be scanned, c opied or duplicated, or posted to a publicly accessible web site, in whole or in part. CHAPTER P Preparation for Calculus Section P.1 Graphs and Models 1. To find the x-intercepts of the graph of an equation, let y be zero and solve the equation for x. To find the y-intercepts of the graph of an equation, let x be zero and solve the equation for y. 2. Symmetry helps in sketching a graph because you need only half as many points to plot. Answers will vary. 3. 3
23 yx=− + x-intercept: ()2, 0 y-intercept: ()0, 3 Matches graph (b). 4. 29 yx=− x-intercepts: () ( )3, 0 , 3, 0− y-intercept: ()0, 3 Matches graph (d). 5. 23 yx=− x-intercepts: () () 3, 0 , 3, 0 − y-intercept: ()0, 3 Matches graph (a). 6. 3yx x=− x-intercepts: () ( ) ( )0, 0 , 1, 0 , 1, 0 − y-intercept: ()0, 0 Matches graph (c). 7. 1
22 yx=+ 8. 52 yx=− 9. 24 yx=− 10. ()23 yx=− x 4− 2− 0 2 4 y 0 1 2 3 4 x 1− 0 1 2 5
2 3 4 y 7 5 3 1 0 1− 3− x 0 1 2 3 4 5 6 y 9 4 1 0 1 4 9 x 3− 2− 0 2 3 y 5− 0 4 0 5− Section P.1 Graphs and Models 3 © 2023 Cengage Learning. All Rights Reserved. May not be scanned, c opied or duplicated, or posted to a publicly accessible web site, in whole or in part. 11. 1 yx=+ 12. 1 yx=− 13. 6 yx=− 14. 2 yx=+ 15. 3yx= 16. 1
2yx=+ 17. 5 yx=− (a) () ( ) () 2, 2, 1.73 5 2 3 1.73yy== − = ≈ (b) () ( ) ( ) () ,3 4 ,3 3 5 4x =− = −− 18. 55 yx x=− (a) () ( )0.5, 0.5, 2.47 y −= − (b) () ( ), 4 1.65, 4x−= − − and() ( ),4 1 ,4x−= − x −4 −3 −2 −1 0 1 2 y 3 2 1 0 1 2 3 x 3− 2− 1− 0 1 2 3 y 2 1 0 1− 0 1 2 x 0 1 4 9 16 y 6− 5− 4− 3− 2− x 2− 1− 0 2 7 14 y 0 1 2 2 3 4 x 3− 2− 1− 0 1 2 3 y 1− 3
2− 3− Undef. 3 3
2 1 x 6− 4− 3− 2− 1− 0 2 y 1
4− 1
2− 1− Undef. 1 1
2 1
4 4 Chapter P Preparation for Calculus © 2023 Cengage Learning. All Rights Reserved. May not be scanned, c opied or duplicated, or posted to a publicly accessible web site, in whole or in part. 19. 25 yx=− y-intercept: () ( )20 5 5 ; 0 , 5 y=− = −− x-intercept: ()55
2202 5
52
;, 0x
x
x=−
=
= 20. 243 yx=+ y-intercept: () ( )240 3 3 ; 0 ,3 y=+ = x-intercept: 2
204 3
34x
x=+
−= None. y cannot equal 0. 21. 22 yx x=+ − y-intercept: ()200 2
2; 0, 2y
y=+ −
=− − x-intercepts: () ( )
() ( )202
02 1
2, 1; 2, 0 , 1, 0xx
xx
x=+ −
=+ −
=− − 22. 234 y xx=− y-intercept: ()
()2304 0
0; 0, 0y
y=−
= x-intercepts: () ()
() ( )304
02 2
0, 2; 0, 0 , 2, 0xx
xx x
x=−
=− +
=± ± 23. 216 yx x=− y-intercept: ()201 6 0 0 ;0 , 0 y=− = x-intercepts: () ()
() () ( )201 6
04 4
0, 4, 4; 0, 0 , 4, 0 , 4, 0xx
xx x
x=−
=− +
=− − 24. ()211 yx x=− + y-intercept: ()
()2010 1
1; 0, 1y
y=− +
=− − x-intercept: ()
()201 1
1; 1, 0xx
x=− +
= 25. 2
51xyx−=+ ()()
()20-intercept: 2 ; 0, 250 1
2-intercept: 051
02
4; 4 , 0yy
xxx
x
x−==+
−=+
=−
= 26. ()2
23
31x xy
x+=
+ y-intercept: ()
()
()2
203 0
30 1
0; 0, 0y
y+=
 +
= x-intercepts: ()
()
()
() ( )2
2
230
31
30
31
0, 3; 0, 0 , 3, 0xx
x
xx
x
x+=
+
+=
+
=− − 27. 2240 xy x y−+ = y-intercept: ()
()2200 4 0
0; 0, 0yy
y−+ =
= x-intercept: () ()
()2204 0 0
0; 0, 0xx
x−+ =
= 28. 221 yx x=− + y-intercept: ()
()220 0 1
1; 0, 1y
y=− +
=− − x-intercept: 2
2
22
2
202 1
21
41
31
1
3
3
3
33;, 033xx
xx
xx
x
x
x
x=− +
=+
=+
=
=
=±
= Note: 33 x=− is an extraneous solution.