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MTH 1000
Test #2
1.
[10pts]
Find the coordinates of the vertex:
f x   3x 2  12 x  5
f x   3x  2  1
2
2.
Determine the end behavior of the following polynomials:
[10pts]
3.
[5pts]
f ( x)  5 x 6  3x  1
Right:
Left:
f ( x)  2 x 3  22 x  48
Right:
Left:
Circle the appropriate equation which matches with the following graph:
f ( x)  x  1x  1
f ( x)  x  1 x  1
2
f ( x)   x  1x  1
2
f ( x)  x  1 x  1
2
2
4.
Divide the following polynomials and find a Quotient and a Remainder:
[5pts]
5.
3x
4
 

 5x 3  4 x  5  x 2  2 x  1
Identify the vertical asymptotes:
[11pts]
f ( x) 
6.
x3
x2  4
f ( x) 
x2  x  2
x 2  2x  3
Identify the horizontal or oblique/slanted asymptotes, if any exist:
[11pts]
f ( x) 
x 2  3x  5
2x3  4x  7
f ( x) 
x2  x  3
x2
7.
Graph the following Rational Function:
f ( x) 
x 2  4x  3
4  x2
[14pts]
Vertical Asymptote(s):
Horizontal/Oblique Asymptote(s):
Determine the region(s) where the rational function is positive/negative.
Combine all this information appropriately to generate the graph of the function.
8.
Solve the following Inequalities:
[14pts]
9
x
9.
x
1
x 2

2
x 1
Find the roots of the following polynomial: f x   2 x 3  3x 2  8 x  3
[14pts]
First, write the complete list of potential numbers that could be zeros according to the
Rational Zeros Theorem:
Now, identify a number from the list above which actually is a root, and then divide to
find the remaining roots of the polynomial: