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

$$z=y^2$$

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 $(4, −2)$.

Describe in words the region of R^3 represented by the equations or inequalities. x^2+y^2+z^2>2z

In this exercise, could the contour diagram represent a linear function?

Find the equation of the surface.

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

Find the equation of the vertical plane perpendicular to the $y$-axis and through the point $(7,8,9)$.

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

A function $f(x, y)$ can be an increasing function of $x$ with $y$ held fixed, and be a decreasing function of $y$ with $x$ held fixed.

The figure shows the parabolas z = f(x, b) for b = -2, -1, 0, 1, 2. Which of the graphs of z = f(x, y) in the figure best fits this information?

Write inequalities to describe the set. The solid cube in the first octant bounded by the coordinate planes and the planes x = 2, y = 2, and z = 2.

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

$$z=4$$

In the following exercise, which of (I)-(IV) lie on the graph of the equation?

I. $(2,2,4)$

II. $(-1,1,0)$

III. $(-3,-2,-1)$

IV. $(-2,-2,4)$

$$x-y=0$$