Begin Game. $ 100 $ 200 $ 300 $ 400 $ 500 PolynomialsRational Functions Exponential Functions Log Functions Anything Goes $ 100 $ 200 $ 300 $ 400 $ 500.

Begin Game

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Polynomials Rational Functions

Exponential Functions

Log Functions

Anything Goes

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Polynomials

Main Board Answer

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Find the Quotient and Remainder of

For this you must use long division to get:

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Polynomials $ 100

Polynomials

Show that x+4 is a factor of

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We can use synthetic division

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Polynomials $ 200

-4 1 4 -7 -23 23 12

-4 0 28 -20 -12

1 0 -7 5 3 0

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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Function Basics $ 400

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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Rational Functions $ 400

The answer is:

Rational Functions

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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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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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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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Anything Goes $ 500

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