Deck 2: Functions and Relations

Question 1

Determine which of the given points are solutions to the given equation.

Answer 1

E

Question 2

Identify the set of values x for which y will be a real number.

Answer 2

A

Question 3

Determine which of the given points are solutions to the given equation.

Answer 3

D

Question 4

An x-intercept of a graph has a y-coordinate .

Question 5

In a rectangular coordinate system, the point where the x- and y-axes meet is called the
.

Question 6

Find the midpoint of the line segment whose endpoints are the given points.

Question 7

Find the exact distance between the points.
(-9, 4) and (-5, -6)

A) 116
B) 200
C)
D)

Question 8

The midpoint of the line segment with endpoints ( ) is given by the formula
.

Question 9

Identify the set of values x for which y will be a real number.

Question 10

Find the midpoint of the line segment whose endpoints are the given points.
(-24.6, 38.1) and (-25.7, -17.7)

A) (0.55, 27.9)
B) (-25.15, 10.2)
C) (6.75, -21.7)
D) (-25.15, 27.9)

Question 11

The x- and y-axes divide the coordinate plane into four regions called .

Question 12

A y-intercept of a graph has an x-coordinate of .

Question 13

Find the midpoint of the line segment whose endpoints are the given points.

Question 14

The distance between two distinct points ( ) is given by the formula
.

Question 15

Given an equation in the variables x and y, find the y-intercept by substituting for x
and solving for .

Question 16

Find the midpoint of the line segment whose endpoints are the given points.

Question 17

A to an equation in the variables x and y is an ordered pair (x, y) that makes the
equation a true statement.

Question 18

Find the exact distance between the points.

Question 19

Choose the one alternative that best completes the statement or answers the question.
Plot the point on a rectangular coordinate system.

Question 20

Determine if the given points form the vertices of a right triangle.
(-3, 5), (-1, 3), and (-4, 0)

A) No
B) Yes

Question 21

Graph the equations on the standard viewing window.

Question 22

Graph the equation with a graphing utility on the given viewing window.

Question 23

Determine the x- and y-intercepts of the graph whose points are defined in the table.

Question 24

Graph the equation by plotting points.

Question 25

Find the x- and y-intercepts.

Question 26

Find the center of a circle if a diameter of the circle has the given endpoints.

Question 27

Solve the problem.

Question 28

Estimate the x- and y-intercepts from the graph.

Question 29

Graph the equation by plotting points.

Question 30

Estimate the x- and y-intercepts from the graph.

Question 31

Find the x- and y-intercepts.

Question 32

An isosceles triangle is shown. Find the area of the triangle. Assume that the units shown in the grid are
in meters.

Question 33

Solve the problem.
The figure represents the average credit card debt for selected households in Silerville. Let y represent the credit card debt in dollars. Let x represent the year, where x = 0 corresponds to the year 1990, x = 4 represents 1994, and so on.

A) Use the ordered pairs given in the graph, (0, 3844) and (16, 8304) to find a linear equation to estimate the
Average credit card debt versus the year. Round the slope to the nearest tenth.
B) Use the model from (a) to estimate the average debt in 1,997. Round to the nearest dollar.

Question 34

Assume that the units shown in the grid are in feet.
a. Determine the exact length and width of the rectangle shown.
b. Determine the perimeter and area.

Question 35

Find the x- and y-intercepts.

Question 36

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
A is the set of all points in a plane equidistant from a fixed point called the
.

Question 37

Solve the problem.

Question 38

Graph the equation with a graphing utility on the given viewing window.

Question 39

The endpoints of a diameter of a circle are shown. Find the center and radius of the circle.

Question 40

Graph the equation by plotting points.

Question 41

Use the given information about a circle to find its equation.

Question 42

Use the given information about a circle to write an equation of the circle in standard form. Graph the
circle.

Question 43

Use the given information about a circle to find its equation.

Question 44

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.

A) No
B) Yes

Question 45

Find an equation of the circle with the given characteristics.

Question 46

Determine the center and radius of the circle.

Question 47

Use the given information about a circle to write an equation of the circle in standard form.

Question 48

Solve the problem.

Question 49

Determine the center and radius of the circle.

Question 50

Find an equation of the circle with the given characteristics.

Question 51

Find an equation of the circle with the given characteristics.

Question 52

Use the given information about a circle to write an equation of the circle in standard form.

Question 53

Use the given information about a circle to write an equation of the circle in standard form.

Question 54

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The distance from the center of a circle to any point on the circle is called the and is
often denoted by r.

Question 55

Find an equation of the circle with the given characteristics.

Question 56

Identify the center and radius of the circle.

Question 57

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
An equation of a circle written in the form = 0 is called the form of an equation of a circle.

Question 58

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The standard form of an equation of a circle with center (h, k) and radius r is given by
.

Question 59

Solve the problem.

Question 60

Use the given information about a circle to find its equation.

Question 61

Write the equation in standard form: . Then, if possible, identify the center and
radius of the circle. If the equation represents a degenerate case, give the solution set.

Question 62

Solve the problem.
A cell tower is a site where antennas, transmitters, and receivers are placed to create a cellular network. Suppose that a cell tower is located at a point A(-7, -6) on a map and its range is 2.5 mi.
Write an equation that represents the boundary of the area that can receive a signal from the tower.
Assume that all distances are in miles.

Question 63

Write the equation in standard form: . Then, if possible, identify the center and
radius of the circle. If the equation represents a degenerate case, give the solution set.

Question 64

Solve the problem.
Find the shortest distance from the origin to a point on the circle defined by

Question 65

Write the given equation in the form . Identify the center and radius.

Question 66

Write the equation in standard form to find the center and radius of the circle. Then sketch the graph.

Question 67

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Explain what it means for a relation to define y as a function of x.

Question 68

Write the given equation in the form . Identify the center and radius.

Question 69

Write the equation in standard form to find the center and radius of the circle.

Question 70

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
A set of ordered pairs (x, y) is called a in x and y. The set of x values in the relation is
called the of the relation. The set of values is called the range of the
relation.

Question 71

Write the given equation in the form . Identify the center and radius.

Question 72

Write the given equation in the form . Identify the center and radius.

Question 73

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Given a function defined by y = f (x), the statement f (2) = 4 is equivalent to what ordered pair?

Question 74

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
If the graph of a set of points (x, y) has two points aligned vertically then the relation (does/does not)
define y as a function of x.

Question 75

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Given a function defined by y = f (x), to find the x-intercept(s), substitute 0 for and
solve for x.

Question 76

Write the given equation in the form . Identify the center and radius.

Question 77

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Given a function defined by y = f (x), to find the -intercept, evaluate f (0).

Question 78

Identify the center and radius of the circle.

Question 79

Write the given equation in the form . Identify the center and radius.

Question 80

Determine the solution set for the equation.