Sketch a graph of the surface and briefly describe it in words.

$$2 x+4 y+3 z=12$$

Suppose that $z$ is a linear function of $x$ and $y$ with slope $2$ in the $x$-direction and slope $3$ in the $y$-direction.

(a) A change of $0.5$ in $x$ and $-0.2$ in $y$ produces what change in $z?$

Is the statement true or false? Give reason for your answer.

A function $f(x, y)$ can have the property that $g(x)=$ $f(x, 5)$ is increasing, whereas $h(x)=f(x, 10)$ is decreasing.

For this exercise, match the given contour diagrams with the surfaces. Give reasons for your choice.

Find an equation for the plane containing the line in the $x y$-plane where $y=1$, and the line in the $x z$-plane where $z=2$.

Match the Cobb-Douglas production function below with a graph in the given figure and a statement.

$$F(L, K)=L^{0.25} K^{0.25}$$

Sketch graph of the equation in $3$-space.

$$y=1$$

Find the equation of the linear function $z=c+m x+n y$ whose graph contains the points $(0,0,0),(0,2,-1)$, and $(-3,0,-4).$

Sketch a contour diagram for the function with at least four labeled contours. Describe in words the contours and how they are spaced. $f(x, y)=y-x^2$

Sketch a contour diagram for the function with at least four labeled contours. Describe in words the contours and how they are spaced. f(x, y)=3x+3y

Find an equation for the contour of $f(x, y)=2x^2y+6x+25$ that goes through the point $(4, −2)$.

For this exercise, match the given contour diagrams with the surfaces. Give reasons for your choice.

Match the pairs of functions with the given contour diagrams. Which contours represent f and which represent g? (The x - and y-scales are equal.)

$$f(x, y)=x^2-y^2, g(x, y)=x y$$

Find the equation of the surface.

A cylinder of radius $\sqrt{7}$ with its axis along the $y$-axis.