calculus

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Instructions: Solve the following problems, showing all of your work for full credit . Problem 1: (10 Points) (A)

Given 73

1 ))(()(

+ ==

x xgfxh 

Find i) )(xf ii) )(xg

(B) For the function given below, construct and simplify the difference of Quotient a) 42)( 2 −= xxf MA112/109

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Problem 2: (20 Points) A) . Consider the parabola of equation 56)( 2 +−= xxxf a) Find the vertex by completing the square b) Find the axis of symmetry c) Find i) x- intercept ii) y-intercepts d) Sketch the graph of ( )f x

MA112/109 EXAM II

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Problem 3: (15 Points)

Given   

≥+ <+−

= 1,1 1,13

)( 2 xifx xifx

xf

a) Find i) )1(−f = ii) )0(f = iii) )1(f iv) )2(f = b) Sketch an accurate graph of f

MA112/109

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Problem4: (15 Points) (A) Write the equation of the function that has the shape of 3xy = , but shifted left 3 units and up 4 units (B)

Find the exact solution: 3

9 3

2

− =

− xx x

- (C) Solve and write the interval notation for the solution set and graph solution set Solve: 215 ≥+ x

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Problem 6; f (x) = x+2 and g(x) = 1−x , find each of the following. (5 points) a) Domain of f(x): b) Domain of g(x): c) Domain of (f + g) (x): d) Find (f/g)(x) = e) Domain of (f/g)(x) = Problem 7: (5, Points) Given functions: 13)( += xxf , 62)( 2 −−= xxxg and 2)( xxh =

a) Find ( )( )xgfxk =)(

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b) Find ( )( )2)( hfxl = Problem 8: Graph the following function: (5 points)

 

 



 

 



> ≤≤−−

−<−

= 2,5

2,2, 2,2

)( 2

xfor xforx

xforx xf

Table Here

Problem 9: (5 point)

a) Determine whether the graph 35)( xxxf −= is symmetrical with respect to the x-axis, the y-axis and/or the origin. Show your work.

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b) Which of the following function is even or odd function? Show your work

a) 216)( xxf −= b) 32)( xxf =