MATH 3208 MIDTERM REVIEW. (B) {x 4 x 5 ; x ʀ} (D) {x x ʀ} Use the given functions to answer questions # 3 5. determine the value of h(7).

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1 MATH 08 MIDTERM REVIEW. If () = (f + g)() wat is te domain of () { 5 4 ; ʀ} { 4 4 ; ʀ} { 4 5 ; ʀ} { ʀ}. Given p() = and g() = wic function represents k() k() = p() g() + + Use te given functions to answer questions # 5. g() = p() = q() =. Given ( ) g( ) q( ) determine te value of (7) Wic function represents k() k() = p()q() k() = k() = k() = k() = 5. Wat is te domain of r() { ʀ} { ; ʀ} p( ) r( ) g( ) { ; ʀ} { ; ; ʀ}. Given f() = and g() = f. Determine te non permissible values of te grap of y () g ± none 7. Given te functions f() = 4 and g() = + +. Determine te value of f(g( )) Given te functions g() = + 5 and () =. Wic function represents ( g )( ) Given p ( ) and q() = + wat is te range of te composite function q(p()) { y y 0 ; yʀ} { y y ; yʀ} { y y ; yʀ} { y y ; yʀ} 0. Wic function represents f(g()) f ( ) and g( )

2 . Wic statement is FALSE for te grap of te function 4 y Te y intercept is 4. Te intercept is. Te orizontal asymptote is y =. Te vertical asymptote is =.. Wat is te point of discontinuity of te function y (, ) (, ) (, 5 ) (, 5 ). Given te functions f ( ) 4, g ( ), ( ), k( ). Determine te following composite functions and state teir domain and range. (a) g(f()) (b) (g()) (c) k(g()) 4. Sketc te grap of te function y. Identy te important caracteristics 8 5 of te grap by completing te table below. 0 y Caracteristic y 8 5 Domain Range Equation of Vertical Equation of Horizontal Non Permissible Value(s) Sketc te grap of te function y. Identy te important caracteristics 4 of te grap by completing te table below. y Caracteristic y 4 Domain Range Equation of Vertical Equation of Horizontal Non Permissible Value(s) -0

3 Use te given functions to answer questions # 8. g() = + p() = 4 q() = +. Given ( ) g( ) q( ) determine te value of ( 5) Wat is te domain of r() { ʀ} { > 4 ; ʀ} g( ) r( ) p( ) { 4 ; ʀ} { 4 ; ʀ} 8. Wat is te range of k() k() = q(p()) { y yʀ} { y y 0 ; yʀ} { y y ; yʀ} { y y ; yʀ} 9. Given te functions f() = and g() =. Determine te value of f(g( )) Given f() = + and g() = 4. Determine te non permissible values of te grap g of y () f = =, = ± =. Wic function represents ( g f )( ) f ( ) and g ( ). Wic statement is TRUE for te grap of te function 5 y 9 Te y intercept is 9. Te intercepts are, 5. Te orizontal asymptote is y =. Te vertical asymptote is =.. Wat is te point of discontinuity of te function y 5 (, ) (, 5 ) (, ) (, 5 ) 4. Given te functions f ( ), g ( ), ( ) 4, k ( ). Determine te following functions and state teir domain and range. (a) f(g()) (b) (g()) (c) k(g())

4 0 5. Sketc te grap of te function y. Identy te important caracteristics of te grap by completing te table below. y 0 Caracteristic y 0 5 Domain Range Equation of Vertical Equation of Horizontal Non Permissible Value(s) -0. Evaluate te its. (a) 4 (b) (c) 0 8 (d) (e) (f) (g) sin7 0 sin () tan 4 sin 0 7. Wat is te domain of te function f ( ) (, 0 ) U ( 0, ) U (, ) (, ) U (, 0 ) U ( 0, ) (, ) U (, ) U (, ) (, ) 8. Wat are te intervals of increase for te function graped below (, ) U (, 0 ) (, ) U ( 0, ) (, 0 ) U (, ) ( 0, ) U (, )

5 9. Evaluate te it: Evaluate te it: 0 0 does not eist. Evaluate te it: 4. Evaluate te it: 4 4 does not eist. Evaluate te it: 0 does not eist Use te given grap to answer questions # Determine te value of f( ). 0 undefined 5. Evaluate te it: f ( ) 0. Evaluate te it: f ( ) 0 does not eist

6 7. Given f ( ) on wic interval(s) is te function f() continuous 8 (, ] U [ 4, ) (, ) U ( 4, ) [, 4 ] (, 4 ) 8. Wic function as a removable discontinuity at = 4 f ( ) 9 4 f ( ) 9 f ( ) 9 f ( ) 9 9. Wic statement is TRUE for te piecewise function f ( ) Te value of f( ) =. Te function is left continuous at =. Te value of f() = 5. Te function is rigt continuous at =. 40. Wic statement is FALSE for te function 5 f ( ) 4 Te point of discontinuity is,. Te vertical asymptote is =. 4 Te intercept is. Te orizontal asymptote is =. 4. Wat is te oblique asymptote of te function 7 f ( ) y = y = y = 8 y = 9 4. Evaluate te it: Determine te orizontal asymptote of te function f ( ). y = y y does not eist 44. Sketc te grap of te given function and evaluate f ( ). 4 f ( ) 45. Evaluate te following its. 0 (a) (b) (c) sin (5) 0 cos ()

7 0 4. Given te function f ( ), using te definition of continuity 9 0 determine all points at wic f() is discontinuous. Classy any discontinuities as removable or non removable. Sow your it workings to very your answer. 47. Determine te equation of all orizontal asymptotes and all vertical asymptotes of te following functions. For vertical asymptotes, determine te beavior of te function as it approaces te vertical asymptote from eac side. (a) 5 f ( ) (b) 4 5 f ( ) Wic is te correct it definition of te derivative for te function f() =. [( ) 0 ( )] [ ] [( ) 0 ( )] [ ] [( ) 0 ( )] [ ] [( ) 0 ( )] [ ] 49. Given f ( ), determine te domain of f (). { > ; ʀ} { ; ʀ} { > ; ʀ} { ; ʀ} 50. Wic function is dferentiable at te given value f ( ) 5 f ( ) 5 f ( ) 5 f ( ) 5 5. Wat is te slope of te tangent line on te curve y at = 4 dy 5. Given y, determine. d dy dy dy d d d dy d 5. Dferentiate y = sin cos. y= cos sin y= cos + sin y= cos sin y= cos + sin

8 d 54. Evaluate: d 55. Determine te equation of te normal line tat passes troug te curve y at (, ). y = y = + y y d y 5. Determine d for te function y = ( + )( + ) Wat are te points on te curve f() = were te tangent line as a slope of 5 (, 0 ) and ( 5, 0 ) (, 5 ) and ( 5, 5 ) (, 7 ) and ( 5, 5 ) ( 5, 5 ) and (, 5 ) 58. A toy rocket takes off from te ground and travels te pat represented by (t) = t + 8t + 9t were is eigt in meters and t is time in seconds. Wat is te acceleration of te rocket at seconds m/sec 4 m/sec m/sec 0 m/sec 59. Given f ( ), determine f (). f () = f () = 4 f () = 4 f () = 0. Dferentiate: ( 4 ) ( ) ( 4 ) ( 4 ) ( 4 ). Dferentiate: sin( cos + ) ( sin ) cos( cos + ) ( sin ) sin( cos + ) ( + sin ) cos( cos + ) ( + sin ) sin( cos + ). Dferentiate: 4 4. Given te function f() =. (a) Use te Limit Definition of te Derivative to determine f (). (b) Very your answer in part (a) by using te Quotient Rule. 4. Determine te equation of te tangent line at = on te curve y.

9 5. Dferentiate te following functions. (a) 4 y (b) y = ( + )( + ) 4 (c) 4 y ( ). Wic is te correct it definition of te derivative for te function f ( ). 5 0 ( ) 5 ( ) 5 0 ( ) 5 ( ) 5 0 ( 5( ) ) 5 0 ( ) 5 ( ) 5 7. Wic value of k will make te given function dferentiable k f ( ) k = k = k = 4 k = 4 8. Wat is te slope of te tangent line on te curve y at = 8 9. Given y determine dy. d dy 4 d dy 4 d dy 4 d dy 4 d 70. Dferentiate y = sin + cos. y= cos sin y= cos sin y= cos + sin y= cos + sin 7. Wat are te points on te curve f() = 4 were te tangent line as a slope of 0 (, 0 ) and (, 0 ) (, ) and (, ) ( 4, 0 ) and ( 4, 0 ) ( 4, ) and ( 4, ) 7. A toy rocket takes off from te ground and travels te pat represented by (t) = t + 5t + 9t were is eigt in meters and t is time in seconds. Wat is te acceleration of te rocket at seconds m/sec 4 m/sec m/sec m/sec d y 7. Determine d for te function y = ( + )( + )

10 74. Determine te slope of te normal line tat passes troug te curve y at =. 75. Dferentiate: ( + ) ( + ) + 5 8( + ) + 5 4( + ) + 5 4( + ) Given f ( ), determine f () Dferentiate: cos( sin ) sin( sin ) sin( sin ) sin( sin ) sin( sin ) 78. Dferentiate: 79. Determine y: y + + y = 4 y y= y y= y y= y= 80. Use te Limit Definition of te Derivative to determine f () for te function f() = Determine te equation of te tangent line at = on te curve y. 8. Dferentiate te following functions. (a) f() = ( + )( + ) (b) ( ) y 8. Use implicit dferentiation to find te equation of te normal line to y = y at (, ).