Question 1

Which of the following best describes the domain of the function $$f(x, y) = \frac{x^2$ + y^2$}{x - 1}$$?

Accepted Answer

All real numbers $$(x, y)$$ except where $$x = 1$$

Question 2

Given the function $$g(x, y) = \ln(y^2$ - x)$$, what is the domain of $$g$$?

Accepted Answer

All $$(x, y)$$ such that $$y^2 - x$$ \u003e 0$$

Question 3

For the function $$f(x, y) = \sqrt{9 - x^2$ - y^2$}$$, which of the following describes its range?

Accepted Answer

$$0 \leq f(x, y) \leq 3$$

Question 4

Which of the following is the equation for a level curve of the function $$f(x, y)$$?

Accepted Answer

$$f(x, y) = k$$

Question 5

A function of the form $$f(x, y) = ax + by + c$$ represents which geometric object?

Accepted Answer

A plane

Question 6

Suppose $$f(x, y) = \sqrt{9 - x^2$ - y^2$}. $$What is the domain of $$f$$?

Accepted Answer

All $$(x, y)$$ such that $$x^2$$ + $$y^2$$ \leq 9$$

Question 7

Which of the following statements about the range of a function of two variables is correct?

Accepted Answer

The range is the set of all possible output values $$f(x, y)$$ for $$(x, y) in $$the domain.

Question 8

If $$f(x, y) = ax + by + c$$, which equation describes the graph of $$f in $$three-dimensional space?

Accepted Answer

$$z = ax + by + c$$

Question 9

Which of the following is a correct interpretation of a level curve for a function $$f(x, y) in a $$real-world context?

Accepted Answer

A contour line on a topographic map representing points of equal elevation.

Question 10

Given $$f(x, y) = \frac{x^2$ + y^2$}{x - 1}$$, what is the value of $$f(3, 2)$$?

Accepted Answer

$$\frac{13}{2}$$

Question 11

For the function $$g(x, y) = \ln(y^2$ - x)$$, which of the following points is in the domain?

Accepted Answer

$$(1, 2)$$

Question 12

Which of the following best describes the set of level curves for $$f(x, y) = x^2$ + y^2$?

Accepted Answer

Concentric circles centered at the origin

Question 13

If $$f(x, y) = ax + by + c$$ and $$a, b, c$$ are real constants, which of the following is true about the graph of $$f$$?

Accepted Answer

It is a plane in three-dimensional space.

Question 14

Which of the following is NOT a possible domain for a function of two variables?

Accepted Answer

All $$(x, y)$$ such that $$x^2$$ + $$y^2$$ \u003c 0$$

Question 15

Suppose $$f(x, y) = \sqrt{9 - x^2$ - y^2$}$$ models the maximum safe dosage of a medication based on two variables $$x$$ and $$y. $$What does the boundary $$x^2$$ + $$y^2 = 9$ represent?

Accepted Answer

The maximum allowable combined value of $$x$$ and $$y$$ for safe dosage.

Question 16

Which of the following is true about the function $$f(x, y) = \frac{x^2$ + y^2$}{x - 1}$$?

Accepted Answer

It is undefined when $$x = 1.$$

Question 17

If $$f(x, y) = x^2$ + y^2$, what is the level curve for k = 4$?

Accepted Answer

$$x^2$$ + $$y^2 = 4$

Question 18

Which of the following functions has a domain that is all real numbers $$(x, y)$$?

Accepted Answer

$$f(x, y) = ax + by + c$$

Question 19

Which of the following best describes the graph of $$f(x, y) = \sqrt{9 - x^2$ - y^2$}$$?

Accepted Answer

The upper hemisphere of a sphere of radius 3 centered at the origin

Section 4.1 - Functions of Several Variables

Guida di studio - Domande di pratica

Study guide - Flashcard