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This quiz tests the work covered in Lecture 5 and corresponds to the first half of Section 1.6 of the textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et al.).

You may wish to start reviewing the section on powers at http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/zoo/powers.html and then continue to http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/zoo/polynomials.html, both pages have useful graphics.

There is a puzzle at http://www.univie.ac.at/future.media/moe/tests/fun1/erkennen.html which gets you to match quadratic and linear graphs to their formulae.

There are some java applets at http://id.mind.net/ zona/mmts/functionInstitute/polynomialFunctions/graphs/polynomialFunctionGraphs.html which let you play with the coefficients of polynomials of various degrees. This gives a very good idea of how the coefficients change the graph.

Question 1

Question 2

a)		is a polynomial of degree 3 with leading coefficient 7.
b)		is a polynomial of degree 7 with leading coefficient 3.
c)		is a polynomial of degree 4 with leading coefficient 17.
d)		is a polynomial of degree 4 with leading coefficient -5.
e)		is not a polynomial.
f)		is a polynomial of degree 2 with leading coefficient 2.

 

There is at least one mistake.
For example, choice (a) should be true.

The highest power of is 3 and this is degree of the polynomial and the coefficient of is 7 and this is the leading coefficient.

There is at least one mistake.
For example, choice (b) should be false.

Try again, read the definition of a polynomial on page 38.

There is at least one mistake.
For example, choice (c) should be false.

Try again, read the definition of a polynomial on page 38.

There is at least one mistake.
For example, choice (d) should be true.

The highest power of is 4 and this is degree of the polynomial and the coefficient of is -5 and this is the leading coefficient.

There is at least one mistake.
For example, choice (e) should be true.

In a polynomial the powers of must be positive.

There is at least one mistake.
For example, choice (f) should be false.

Try again, read the definition of a polynomial on page 38.

Your answers are correct

1. True. The highest power of is 3 and this is degree of the polynomial and the coefficient of is 7 and this is the leading coefficient.
2. False. Try again, read the definition of a polynomial on page 38.
3. False. Try again, read the definition of a polynomial on page 38.
4. True. The highest power of is 4 and this is degree of the polynomial and the coefficient of is -5 and this is the leading coefficient.
5. True. In a polynomial the powers of must be positive.
6. False. Try again, read the definition of a polynomial on page 38.

Question 3

Not correct. Choice (a) is false.

Try again, the maximum number of turns is one less than the minimum possible degree.

Your answer is correct.

There are 4 turns so the minimum possible degree is 5. Since it is an odd power and the graph tends to as the leading coefficient is negative.

Not correct. Choice (c) is false.

Try again, the graph tends to as and there are 4 turns.

Not correct. Choice (d) is false.

Try again, the graph tends to as

Question 4

Consider the 4 graphs below, which gives global views of the functions, and match them to possible formulae.

a)		= = = =		b)		= = = =
c)		= = = =		d)		= = = =

 

Your answer is correct.

Not correct. Choice (b) is false.

Try again, has to be of even degree and has to be of odd degree.

Not correct. Choice (c) is false.

Try again, some of the formulae do not match any functions. Try expanding the factors.

Not correct. Choice (d) is false.

Try again, some of the formulae do not match any functions. Try expanding the factors.