This quiz tests the work covered in the lecture on graphs of functions of two
variables and corresponds to Section 12.2 of the textbook Calculus: Single and
Multivariable (Hughes-Hallett, Gleason, McCallum et al.).

There is not as much information on the web on functions of two variables as there is
on functions of one variable. There are a few interesting sites. You can start at
http://www.ucl.ac.uk/Mathematics/geomath/level2/pdiff/pd5.html. It refers to an earlier example
which you can find at http://www.ucl.ac.uk/Mathematics/geomath/level2/pdiff/pd21.html.

There is a nice applet at http://www-math.mit.edu/18.02/applets/FunctionsTwoVariables.html which allows you to type in a function or select one from the drop down list and it plots the graph.

There are more web quizzes at Wiley, select Section 2. It now only has 5 questions instead of the usual 15.

*There is at least one mistake.*

For example, choice (a) should be False.

*There is at least one mistake.*

For example, choice (b) should be True.

*There is at least one mistake.*

For example, choice (c) should be True.

*There is at least one mistake.*

For example, choice (d) should be True.

*There is at least one mistake.*

For example, choice (e) should be False.

*Correct!*

*False*$f\left(-1,2\right)={\left(-1\right)}^{2}+{2}^{2}-2\times -1\times 2-3=1+4+4-3=6$ so the point $\left(-1,2,6\right)$ is on the graph and $\left(-1,2,5\right)$ is not on the graph.*True*$f\left(2,-2\right)={2}^{2}+{\left(-2\right)}^{2}-2\times 2\times -2-3=4+4+8-3=13$ so $\left(2,-2,13\right)$ is on the graph.*True*$f\left(1,\pi \right)=1\times sin\pi =1\times 0=0$ so $\left(1,\pi ,0\right)$ is on the graph.*True*$f\left(0,0\right)=-{e}^{-0}=-1$ so $\left(0,0,-1\right)$ is on the graph.*False*$f\left(1,5\right)=2\times 1=2$ so so the point $\left(1,5,2\right)$ is on the graph and $\left(1,5,7\right)$ is not on the graph.

*Choice (a) is incorrect*

*Choice (b) is correct!*

*Choice (c) is incorrect*

*Choice (d) is incorrect*

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is correct!*

Which one of the following describes the function $z=g\left(x,y\right)={\left(x-1\right)}^{2}-{\left(y+2\right)}^{2}+4$ most accurately? Exactly one option must be correct)

*Choice (a) is correct!*

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is incorrect*