Question 1

Given the points $$A(2, -3)$$ and $$B(-4, 5)$$, what is the distance between them? Use the distance formula.

Accepted Answer

$$\sqrt{(2+4)^2$ + (-3-5)^2$} = \sqrt{36 + 64} = \sqrt{100} = 10$$

Question 2

Which of the following equations represents a circle with center at $$(1, -2)$$ and radius $$5$$?

Accepted Answer

$$(x-1)^2$$ + $$(y+2)^2 = 25$

Question 3

Given the equation $$x^2$$ + $$y^2 + 4x - 6y = 12$, what is the center and radius of the circle?

Accepted Answer

Center $$(-2, 3)$$, radius $$5$$

Question 4

Which of the following relations is NOT a function?

Accepted Answer

$$\{(1,2), (2,3), (1,4)\}$$

Question 5

What is the domain of the relation $$\{(-4, -2), (-1, 0), (1, 2), (3, 5)\}$$?

Accepted Answer

$$\{-4, -1, 1, 3\}$$

Question 6

If the equation of a circle is $$x^2$$ + $$y^2 = 16$, what is the radius and center?

Accepted Answer

Center $$(0,0)$$, radius $$4$$

Question 7

A gas station charges $$g$$ dollars for $$x$$ gallons of gas. Which is the independent variable?

Accepted Answer

$$x$$, the number of gallons

Question 8

Given the equation $$y = -2x + 5$$, which of the following is an ordered pair that lies on the graph?

Accepted Answer

$$(0, 5)$$

Question 9

Which of the following best describes the range of the function $$f(x) = x^2$ for x$ in $$[-2, 3]$$?

Accepted Answer

$$[0, 9]$$

Question 10

If a circle has the equation $$(x+2)^2$$ + $$(y-5)^2 = 49$, what is its center and radius?

Accepted Answer

Center $$(-2, 5)$$, radius $$7$$

Question 11

Which of the following statements is TRUE about the graph of $$y = x^2$ + 1$$?

Accepted Answer

It is a parabola opening upwards with vertex at $$(0, 1)$$

Question 12

Given the general form of a circle $$x^2$$ + $$y^2 + Dx + Ey + F = 0$, what is the first step to find its center and radius?

Accepted Answer

Complete the square for both $$x$$ and $$y$$ terms

Question 13

Which of the following is the correct distance between the points $$(7, 11)$$ and $$(-10, -23)$$?

Accepted Answer

$$\sqrt{(7+10)^2$ + (11+23)^2$} = \sqrt{289 + 1156} = 38$$

Question 14

If a relation is given by the set $$\{(2, 5), (3, 7), (2, 8)\}$$, is it a function?

Accepted Answer

No, because the $$x-$$value $$2 is $$repeated with different $$y-$$values

Question 15

Which of the following best describes the range of the relation $$\{(1, 2), (2, 3), (3, 5)\}$$?

Accepted Answer

$$\{2, 3, 5\}$$

Question 16

Given the equation $$x^2$$ + $$y^2 + 2x - 6y = 45$, what is the center and radius of the circle?

Accepted Answer

Center $$(-1, 3)$$, radius $$7$$

Question 17

Which of the following is the correct center-radius form for a circle with center $$(h, k)$$ and radius $$r$$?

Accepted Answer

$$(x-h)^2$$ + $$(y-k)^2$$ = $$r^2$$

Question 18

If the equation $$x^2$$ + $$y^2 + 2x + 2y + 2 = 0$ is given, what can you conclude about its graph?

Accepted Answer

It does not represent a real circle because the radius squared is negative

Question 19

Which of the following best describes the graph of $$y = \sqrt{x+1}$$?

Accepted Answer

It is defined for $$x \geq -1$$ and increases as $$x$$ increases

Rectangular Coordinates, Circles, and Relations in College Algebra

Study Guide - Practice Questions