Since 0, is the remainder , we know x+4 is a factor.
Polynomials
Find a polynomial of degree four, having integer coefficients with zeros 3i and 4, with 4
a double zero.
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Start with :
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Polynomials $ 300
Multiply out to get:
Polynomials
Graph
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The graph should look something like this. Important things to mark are, intercepts, and
end behavior.
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Polynomials
List all zeros of
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This can be factored into:
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Polynomials $ 500
So the zeros are -1, 3, -i, and i
Rational Functions
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Find the x and y intercepts of
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The y-int is:
The x-int’s are:
Rational Functions
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Find the vertical and horizontal asymptotes of
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Rational Functions $ 200
This has a vertical asymptote at x = -4
Since the degree of the top is larger than the degree of the bottom, it does not have a
horizontal asymptote.
Rational Functions
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Analyze the behavior of
Near its vertical asymptotes at x=4, and x=-2
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The answer is:
This says the function will approach positive infinity as x approaches 4 from the right, and -2 from the right. The function will approach negative infinity as x approaches 4 from the left, and -2 from the left.
Rational Functions
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Graph the following function
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The answer is:
Rational Functions
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$ 500
Make a rational function with the following:
• crosses x-axis at -2, and 4
•Has vertical asymptotes at x = -1 and x = 3
•Has a horizontal asymptote at y = 2
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Rational Functions $ 500
One possible answer is to start with:
Then multiply everything out to get:
Exponential Functions
Sketch a graph of the function:
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$ 100
The answer is:
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$ 100Exponential Functions
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Write the following in exponential form
Exponential Functions
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The answer is:
Exponential Functions
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What is the domain and range of the function?
Exponential Functions
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The domain is all real numbers.
The range is (2, infinity)
Exponential Functions
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Find the function
Exponential Function
Whose graph is given
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The answer is:
Exponential Functions
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Find the inverse of:
Exponential Functions
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The answer is:
Exponential Functions
Sketch a graph of the function
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$ 100Log Functions
The answer is:
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$ 100Log Functions
Write the following in logarithmic form
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$ 200Log Functions
The answer is:
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$ 200Log Functions
What is the domain and range of
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$ 300Log Functions
The domain is (-1,infinity)
The range is all real numbers
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$ 300Log Functions
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$ 400
Find the function
Whose graph is given
Log Functions
The answer is:
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$ 400Log Functions
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Find the inverse of
Log Functions
The answer is:
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Anything Goes
Expand the following using the laws of logarithms
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The answer is:
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Anything Goes
Combine the following using the laws of logarithms
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The answer is:
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Anything Goes
Express the following in the form a + bi
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The answer is:
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Anything Goes
If $10,000 is invested at an interest rate of 10% per year, compounded semiannually, find
the value of the investment after the given number of years:
• 5 years
•10 years
•15 years
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The answer is:
5 yrs: $16,288.95
10 yrs: $26,532.98
15 yrs: $43,219.42
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(Disclaimer: For this problem a calculator was handy for doing computations. Since no calculator will be allowed on the exam, I will be
sure to choose a problem with “better” numbers to work with.)
Anything Goes
The following is an except of Joe’s work. Identify, and correct Joe’s mistakes to see the
answer they should have gotten:
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The subtraction was done incorrectly. It should have been -2 circled in red. Later on the subtraction was done incorrectly again, see the blue circle. The correct quotient should actually be 6x – 2