3:57 PM Wed Sep 14 . . . 1 89% webassign.net a 34. [-/0.23 Points] DETAILS SPRECALC7 2.7.028.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use f(x) = 3x - 5 and g(x) = 4 - x2 to evaluate the expression. (a) (b ) g(g(3) ) Need Help? Read It Watch It Master It 35. [-/0.23 Points] DETAILS SPRECALC7 2.7.029.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use f(x) = 2x - 3 and g(x) = 5 - x2 to evaluate the expression. (a) (f . g) (-2) (b) (g . n) (-2) Need Help? Read it Watch It Master it 36. [-/0.23 Points] DETAILS SPRECALC7 2.7.030.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use f(x) = 2x - 5 and g(x) = 3 - x2 to evaluate the expression. ( a ) ( f . D) ( - 1 ) ) (g . g)(-1) Need Help? Read It Watch It Master It 37. [-/0.23 Points] DETAILS SPRECALC7 2.7.033.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the given graphs of f and g to evaluate the expression. (Assume that each point lies on the gridlines.) f(g(4)) =13. [-/0.23 Points] DETAILS SPRECALC7 2.6.039. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations. y=4\\/x 0 Need Help? _ 42. [-l0.23 Points] DETAILS SPRECALC7 2.7.058.Ml. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Consider the following functions. x X+3 f(X) = % 9(X) = Find (f o g)(x). Find the domain of (f o g)(x). (Enter your answer using interval notation.) Find (g o f)(X). Find the domain of (g o f)(x). (Enter your answer Using interval notation.) Find (r a f)(x). Find the domain of (f a f)(x). (Enter your answer using interval notation.) Find (9 a 9000' Find the domain of (g ., g)(x). (Enter your answer using interval notation.) Need Help?| but [I null I] burn I 43. [-/0.23 Points] DETAILS SPRECALC7 2.7.060.Ml. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Find fogoh. f(x) = %, g(x) = x3, h(x) = x + 8 Need Help? 12. [-/0.23 Points] DETAILS SPRECALC7 2.6.034. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations. f ( x ) = (x + 7) 2 10 10 5 5 -LX -X -10 -5 5 10 - 10 -5 5 10 -5 - 5 O -10 O -10 - 4 10 10 51 5 X X -10 -5 5 10 -10 -5 5 10 -5 -5 -10 -10 O Need Help? Read It11. [-IO.23 Points] DETAILS SPRECALC7 2.6.022. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Explain how the graph ofg is obtained from the graph of f. (a) M = . 900 = \\/ + 6 O reflect about the x-axis, then shift up 6 units 0 reflect about the yaxis, then shift down 6 units 0 reflect about the y-axis, then shift up 6 units 0 reflect about the x-axis, then shift down 6 units 0 shift up 6 units, then reflect about the Xaxis (b) rm = J}. g(x) = \\/_x + s 0 reflect about the x-axis, then shift up 6 units 0 reflect about the xaxis, then shift down 6 units 0 reflect about the y-axis, then shift up 6 units 0 reflect about the y-axis, then shift down 6 units 0 shift down 6 units, then reflect about the y-axis Need Help? @ 7. [-l0.23 Points] DETAILS SPRECALC7 2.6.503.XP. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Suppose the graph of fis given. Describe how the graph of each function can be obtained from the graph of f. (a) y=f(x9)+% O shift right 9 units, then stretch vertically by a factor of% 0 shift left 9 units, then shift down % units 0 shift right 9 units, then shift up % units 0 shift right 9 units, then shift down % units 0 shift left 9 units, then shift up % units (b) y=r(x+9)% 0 shift right 9 units, then shift up % units shift left 9 units, then shift up Q units 9 shift right 9 units, then shift down i units 9 0 shift left 9 units, then shift down % units 0 shift left 9 units, then stretch vertically by a factor of% Need Help? _ Submit Answer 8. [IO.23 Points] DETAILS SPRECALC7 2.6.505.XP. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Suppose the graph of fis given. Describe how the graph of each function can be obtained from the graph of f. (a) y = 9 - 4f(X) O stretch vertically by a factor of 4, reflect about the Xaxis, then shift down 9 units O stretch vertically by a factor of 4, reflect about the X-axis, then shift up 9 units 0 stretch vertically by a factor of 4 then shift down 9 units 0 stretch horizontally by a factor of 4, reflect about the Xaxis, then shift up 9 units 0 stretch vertically by a factor of 4, reflect about the y-axis, then shift up 9 units (b) y = 4 - f(-X) 0 reflect about the x-axis, then shift up 4 units 0 reflect about the xaxis, reflect about the y-axis, then shift up 9 units O shift up 4 units, reflect about the Xaxis, then reflect about the yaxis 0 reflect about the X-axis, reflect about the y-axis, then shift up 4 units 0 reflect about the Xaxis, reflect about the yaxis, then shift right 4 units Need Help? __ 3:57 PM Wed Sep 14 . . . 1 89% webassign.net a 44. [-/0.23 Points] DETAILS SPRECALC7 2.8.001. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER A function f is one-to-one if different inputs produce ---Select--- > >outputs. You can tell from the graph that a function is one-to-one by using the --Select--- Test. Need Help? Read It Submit Answer 45. [-/0.23 Points] DETAILS SPRECALC7 2.8.006. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER True or false? (a) If f has an inverse, then f-1(x) is always the same as F(x). O True O False (b) If f has an inverse, then f-1(f(x)) = x. O True O False Need Help? Read It 46. [0.23/0.23 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 2.8.008. 2/5 Submissions Used MY NOTES ASK YOUR TEACHER A graph of a function f is given. 0 Determine whether f is one-to-one. Yes, f is one-to-one. No, f is not one-to-one. Need Help? Read It 47. [0.23/0.23 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 2.8.012. 1/5 Submissions Used MY NOTES ASK YOUR TEACHER A graph of a function f is given.3:57 PM Wed Sep 14 1 E? 89% - webassignhet h 41. [-10.23 Points] DETAILS SPRECALC7 2.7.055.Ml. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Consider the following functions. f(x) = g(x) = 4X 7 x+7' Find (f c. g)(X). Find the domain of (f D g)(x). (Enter your answer using interval notation.) Find (9 .. f)(x). Find the domain of (g D f)(x). (Enter your answer using interval notation.) Find (f D f)(x). Find the domain of (f o f)(x). (Enter your answer using interval notation.) Find (9 . g)(X)- Find the domain of (g a g)(x). (Enter your answer using interval notation.) Need Help?| man [I van-I I] \"I I 42. [-l0.23 Points] DETAILS SPRECALC7 2.7.058.M|. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Consider the following functions. X x+3 f(X) = 3 g(x) = Find (f o 9)(X). Find the domain of (f o g)(x). (Enter your answer using interval notation.) Find (9 o 000. 3:56 PM Wed Sep 14 . . . 1 89% webassign.net a 30. [-/0.23 Points] DETAILS SPRECALC7 2.7.013. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Find f + g, f - g, fg, and f/g and their domains. f( x ) = V 16 - x2, g( x) = x+ 2 Find (f + 9) (x). Find the domain of (f + g)(x). (Enter your answer using interval notation.) Find (f - g)(x). Find the domain of (f - 9)(x). (Enter your answer using interval notation.) Find (fg)(x). Find the domain of (fg)(x). (Enter your answer using interval notation.) Find (x). Find the domain of (x). (Enter your answer using interval notation.) Need Help? Read It Watch It 31. [0.23/0.23 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 2.7.017.MI. 1/5 Submissions Used MY NOTES ASK YOUR TEACHER Find the domain of the function. (Enter your answer using interval notation.) f ( x ) = V x+ v3 - x [0,3 Need Help? Read It Watch It Master It 32. [0.23/0.23 Points DETAILS PREVIOUS ANSWERS SPRECALC7 2.7.504.XP.MI. 1/5 Submissions Used MY NOTES ASK YOUR TEACHER3256 PM Wed Sep 14 on. 1 989%- webassignhet l. Submit Answer 29. [40.23 Points] DETAILS SPRECALC7 2.7.012. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Consider the following functions. f(x) = x2 + 7x, g(x) = 8x2 1 Find (f+ g)(x). Find the domain of (f + g)(x). (Enter your answer using interval notation.) Find (f g)(x). Find the domain of (f g)(x). (Enter your answer using interval notation.) Find (fg)(x). Find the domain of (fg)(x). (Enter your answer using interval notation.) Find (5)0\" Find the domain of (L)(x). (Enter your answer using interval notation.) 9 Need Help? _' 30. [-10.23 Points] DETAILS SPRECALC7 2.7.013. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Find f+ g, f g, fg, and f/g and their domains. f(X)= Viex2, 9(X)= VX+2 Find (r+ g)(x). Find the domain of (f + g)(x). (Enter your answer using interval notation.) Find (r- g)(X). Find the domain of (f g)(x). (Enter your answer using interval notation.) 9. [-IO.23 Points] DETAILS SPRECALC7 2.6.018. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Suppose the graph of fis given. Describe how the graph of each function can be obtained from the graph of f. (a) y = f(2X) - 6 O shrink horizontally by a factor of %, then shift down 6 units O stretch vertically by a factor of 2, then shift up 6 units 0 shrink vertically by a factor of i, then shift up 6 units O stretch horizontally by a factor of 2, then shift down 6 units 0 shrink horizontally by a factor of %, then shift right 6 units me) O stretch horizontally by a factor of 2, then shrink vertically by a factor of% O stretch horizontally by a factor of 2, then stretch vertically by a factor of 2 O shrink horizontally by a factor of %, then stretch vertically by a factor of 2 Q There is no change. 0 shrink horizontally by a factor of i, then shrink vertically by a factor of% Need Help? 10. [-10.23 Points] DETAILS SPRECALC7 2.6.020.Ml. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Explain how the graph ofg is obtained from the graph of f. (a) f(X) = x3, g(x) = (x 3)3 0 shift right 3 units 0 shift left 3 units 0 stretch vertically by a factor of 3 0 shift up 3 units 0 shift down 3 units (b) r(x) = x3. 900 = x3 3 0 shift right 3 units 0 shift down 3 units 0 shift up 3 units O stretch vertically by a factor of 3 0 shift left 3 units Need Help? @@ 3:57 PM Wed Sep 14 . . . 1 89% webassign.net a 40. [-/0.23 Points] DETAILS SPRECALC7 2.7.050.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Consider the following functions. f ( x ) = x3 + 5, g(x) = Vx Find (f . 9) (x). Find the domain of (f . g)(x). (Enter your answer using interval notation.) Find (g . f) (x). Find the domain of (9 . f)(x). (Enter your answer using interval notation.) Find (f . f) (x). Find the domain of (f . f)(x). (Enter your answer using interval notation.) Find (g . g) (x). Find the domain of (9 . g)(x). (Enter your answer using interval notation.) Need Help? Read It Watch It Master It 41. [-/0.23 Points] DETAILS SPRECALC7 2.7.055.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Consider the following functions. f ( x ) = - 9 (x) = 4x - 7 Find (f . g) (x). Find the domain of (f . g)(x). (Enter your answer using interval notation.) Find (g . f) (x).37. [-/0.23 Points] DETAILS SPRECALC7 2.7.033.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the given graphs of f and g to evaluate the expression. (Assume that each point lies on the gridlines.) flg ( 4) ) =[ Need Help? Read It Watch It Master It 38. [-/0.23 Points] DETAILS SPRECALC7 2.7.034.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the given graphs of f and g to evaluate the expression. (Assume that each point lies on the gridlines.) g(f(0) ) = o Need Help? Read it Watch It Master It 39. [-/0.23 Points] DETAILS SPRECALC7 2.7.036.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the given graphs of f and g to evaluate the expression. (Assume that each point lies on the gridlines.) ( f . g ) ( 2 ) = Need Help? Read It Watch It Master It4. [-/0.23 Points] DETAILS 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Match the graph with the function. N -6 2 4 6 -6 -4 -2 2 4 -21 -4/ -4 (I) (II) N -6 -4 -2 2 4 6 -6 -4 -2 2 4 6 -2 -2 -4 -4 -6 (III) (IV) ) y = 1x+ 21 ---Select--- ( b ) y = 1x - 21 ---Select--- (c) y = 1x1 - 2 ---Select--- (d) y = - Ixl ---Select--- Submit Answer14. [lO.23 Points] DETAILS SPRECALC7 2.6.045. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations. y=(x5)2+2 0 Need Help? @- 5. [-l0.23 Points] DETAILS SPRECALC7 2.6.008. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Suppose the graph of fis given. Describe how the graph of each function can be obtained from the graph of f. (a) f(x + 1) 0 shift left 1 unit 0 shift right 1 unit 0 shift up 1 unit 0 shift clown 1 unit 0 stretch vertically by a factor of 1 (b) f(x) + 2 0 shift left 2 units 0 shift right 2 units 0 shift up 2 units 0 shift down 2 units 0 stretch vertically by a factor of 2 Need Help? 6. [IO.23 Points] DETAILS SPRECALC7 2.6.502.XP. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Suppose the graph of fis given. Describe how the graph of each function can be obtained from the graph of f. (a) y = -7f(X) 0 shift clown 7 units 0 shrink by a factor of 7, then reflect about the yaxis 0 Stretch by a factor of 7, then reflect about the y-axis O stretch by a factor of 7, then reflect about the x-axis O shrink by a factor of 7, then reflect about the Xaxis (b) y = %f(X) O stretch by a factor of 7; then reflect about the y-axis r 0 Stretch by a factor of 71 then reflect about the X-axis I O shrink by a factor of %, then reflect about the X'aXlS O shrink by a factor of 7; then reflect about the y'axis I 0 shift down % units Need Help? _'_' 15. [-l0.23 Points] DETAILS SPRECALC7 2.6.048. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations. y=4\\/X+S Y 10 5 / 4....i........i....t_x 4....1........|....L_x 10 -5 5 10 10 -5 5 10 5 -5 10 -10 0 Need Help? _ 21. [-/0.23 Points] DETAILS SPRECALC7 2.6.068.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER The graphs of f and g are given. Find a formula for the function g. g (x) = R(x ) = x2 -6 - X -2 2 6 Need Help? Read It Master It 22. [-/0.23 Points] DETAILS SPRECALC7 2.6.070. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER The graph of y = f (x) is given. Match each equation with its graph. 6 (1 ) 4 (4) f -5 (2) 5 -21 (3 ) ) y = =f (x ) ---Select--- (b) y = -f (x+ 4) ---Select--- (c) y = f ( x - 4)+3 ---Select--- (d) y = f (-x) ---Select---The graph of a function f is given. Sketch the graphs of the following transformations of f. (a) y = f(4x) y 1 O O (b) y = f(1/4x) O O O O27. [-/0.23 Points] DETAILS SPRECALC7 2.7.001. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER From the graphs of f and g in the figure, we find the following. (Assume that each point lies on the gridlines.) (f + g) (2) = (f - g) (2) = (fg) (2) = (! ) (2) = g Need Help? Read It 28. [-/0.23 Points] DETAILS SPRECALC7 2.7.002. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER By definition, (f . g)(x) =? So if g(5) = 9 and f(9) = 21, then (f . g)(5) = Need Help? Read It V ? Submit Answer g(f (x)) f(g(x)) 29 MY NOTES ASK YOUR TEACHER3:58 PM Wed Sep 14 . . . 1 89% webassign.net is one-to-one is not one-to-one Need Help? Read It 52. [-/0.23 Points] DETAILS SPRECALC7 2.8.026.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Assume that f is a one-to-one function. (a) If f(9) = 14, find f -1(14). f -1(14) = (b ) If f -1(64) = 32, find f( 32). f (32 ) = Need Help? Read It Watch It Master It 53. [-/0.23 Points] DETAILS SPRECALC7 2.8.028.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER If g(x) = x2 + 10x with x 2 -5, find g-1(39). Need Help? Read It Master It 54. [0.23/0.23 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 2.8.040.MI. 2/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the Inverse Function Property to determine whether f and g are inverses of each other. f( x) = 9 - 7x; g( x) = -x Of and g are inverses of each other. Of and g are not inverses of each other. Need Help? Read It Watch It Master It 55. [0.23/0.23 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 2.8.502.XP.MI. 1/5 Submissions Used MY NOTES ASK YOUR TEACHER Find the inverse function of f. f ( x ) = 7x+ 3 f-1 ( x ) = Need Help? Read it Master It19. [-/0.23 Points] DETAILS SPRECALC7 2.6.064.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER The graphs of f and g are given. Find a formula for the function g. g ( x ) = g f(x) = 2x3 +X 2 Need Help? Read it Watch It Master It 20. [-/0.23 Points] DETAILS SPRECALC7 2.6.066.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER The graphs of f and g are given. Find a formula for the function g. g (x ) = - 4 2 f(x) = 1x1 + X - 2 2 -2 Need Help? Read It Master It1. [-l0.23 Points] DETAILS SPRECALC7 2.6.001. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Fill in the blank with the appropriate direction (left, right, up, or down). (a) The graph of y = f(x) + 6 is obtained from the graph of y = f(x) by shifting --Select 3 6 units. (b) The graph of y = f(X + 6) is obtained from the graph of y = f(X) by shifting Seiect-- " 6 units. Need Help? _ 2. [-l0.23 Points] DETAILS SPRECALC7 2.6.002. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Fill in the blank with the appropriate direction (left, right, up, or down). (a) The graph of y = f(x) 5 is obtained from the graph of y = f(x) by shifting ---Select--- 0 5 units. (b) The graph of y = f(x 5) is obtained from the graph of y = f(x) by shifting Select 0 5 units. Need Help? _ 3. [-l0.23 Points] DETAILS SPRECALC7 2.6.003. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Fill in the blank with the appropriate axis (Xaxis or yaxis). (a) The graph of y = f(x) is obtained from the graph of y = f(x) by reflecting in the ---Select--- 0 . (b) The graph of y = f(x) is obtained from the graph of y = f(x) by reflecting in the ---Select--- 0 . Need Help? _ 16. [-/0.23 Points] DETAILS SPRECALC7 2.6.509.XP. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER A function fis given, and the indicated transformations are applied to its graph. Write the equation for the final transformed graph. f(x) = x3; shift downward 3 units. y: Need Help? 17. [l0.23 Points] DETAILS SPRECALC7 2.6.056. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER A function fis given, and the indicated transformations are applied to its graph. Write the equation for the final transformed graph. f(X) = W; shift 8 units to the right y: Need Help? 18. [l0.23 Points] DETAILS SPRECALC7 2.6.057. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER A function fis given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. f(x) = |x| ; shift 4 units to the left and shift downward 9 units Need Help