This quiz tests the work covered in Lecture 6 and corresponds to the second half of
Section 1.6 of the textbook Calculus: Single and Multivariable (Hughes-Hallett,
Gleason, McCallum et al.).

There are further web quizzes at Wiley. Choose section 5 from this page.

Be aware that it doesn’t seem to accept the written answers so you will have to check
whether your answers are correct when they print the correct answer. Question 15
didn’t make sense on 7/11/05.

There is a written explanation at http://id.mind.net/ zona/mmts/functionInstitute/rationalFunctions/rationalFunctions.html which covers the material in the text but it also has links to a variety of applets which are all very useful.

If you are still not sure how to draw these graphs yourself you may want to look at http://www.math.csusb.edu/math110/src/rationals/RfIntro.html and after the demo there is a step by step guide to graphing rational functions. It also has an exercise where you get to work out where the appropriate features of the graph lie.

Which of the following set of statements is correct? Exactly one option must be correct)

*Choice (a) is correct!*

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is incorrect*

$y=\frac{3{x}^{2}-12x+9}{{x}^{2}+5x+6}\phantom{\rule{0.3em}{0ex}}.$ Exactly one option must be correct)

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is correct!*

Hence $y=0$ when $x=3$ or $x=1$ and these are the $x$-intercepts.

$y=\frac{3{x}^{2}-12x+9}{{x}^{2}+5x+6}\phantom{\rule{0.3em}{0ex}}.$ Exactly one option must be correct)

*Choice (a) is correct!*

Hence $y$ is undefined when $x=-3$ or $x=-2$ and these are the vertical asymptotes.

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is incorrect*

Note that ${x}^{2}+5x+6=\left(x+3\right)\left(x+2\right)\phantom{\rule{0.3em}{0ex}}.$

*Choice (a) is incorrect*

Remember horizontal asymptotes are of the form $y=b\phantom{\rule{0.3em}{0ex}}.$

*Choice (b) is incorrect*

*Choice (c) is correct!*

*Choice (d) is incorrect*

but even if they couldn’t be factorized it would make no difference,

we could still find the horizontal asymptote.