Functions And Surfaces

(requires JavaScript)

1. Match functions with their graphs, explain.

   1. $f<!--FUNCTION\; APPLICATION-->\left(x,y\right)=\left|x\right|+\left|y\right|$
   2. $f<!--FUNCTION\; APPLICATION-->\left(x,y\right)=\left|xy\right|$
   3. $f<!--FUNCTION\; APPLICATION-->\left(x,y\right)={\displaystyle \frac{1}{1+x^2+y^2}}$
   4. $f<!--FUNCTION\; APPLICATION-->\left(x,y\right)={\left(x^2-y^2\right)}^2$
   5. $f<!--FUNCTION\; APPLICATION-->\left(x,y\right)={\left(x-y\right)}^2$
   6. $f<!--FUNCTION\; APPLICATION-->\left(x,y\right)=\sin <!--FUNCTION\; APPLICATION-->\left(\left|x\right|+\left|y\right|\right)$

   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   c, e, a, b, f, d
2. Use traces to sketch the surface $y=z^2-x^2$.
3. 1. What does the equation $x^2+y^2=1$ represent in ${ℝ}^2$?
   2. What does it represent in ${ℝ}^3$?
   3. What does the equation $x^2+z^2=1$ represent in ${ℝ}^3$?
   1. A circle of radius $1$ centered at the origin.
   2. A circular cylinder of radius $1$ with axis the $z\text{-axis}$.
   3. A circular cylinder of radius $1$ with axis the $y\text{-axis}$.