Basics

Let $f(x,y) = x^2 e^{3xy}$.

• Evaluate $f(1,1)$.
• Evaluate $f(e,1)$.
• Find and sketch the domain of $f$.
• Find the range of $f$.

Find and sketch the domain of $f(x,y) = \sqrt{y-x} \ln(y+x).$

Level Surfaces

Describe the level surfaces of the function $f(x,y,z) = x^2 -y^2 + z^2$

Describe the level surfaces of the function $f(x,y,z) = x^2 -y^2$

Relationships:

Describe how the graph of $g$ is obtained from the graph of $f$:

• $g(x,y) = f(x-2,y)$
• $g(x,y) = f(x+3,y-4)$
• $g(x,y) = 4 f(x,y)$
• $g(x,y) = 1 - f(x,y)$