calculus

here you see attached.

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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 +−= xx

xf

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 =