Deck 2: Functions

Question 1

Find the center and radius of the circle. $x ^ { 2 } - x + \frac { 1 } { 2 } + y ^ { 2 } - y = \frac { 1 } { 4 }$

Answer 1

Center (1/2, 1/2),
$r = 1 / 2$

Question 2

Find the approximate solution(s) of the equation
in the interval
by drawing a graph in an appropriate viewing rectangle. State each answer correct to two decimals.

Answer 2

Question 3

Find the distance between the points (4,7) and (8,11).

Answer 3

5

Question 4

Calculate the y-coordinates in the table below for the function $y = 3 x ^ { 2 } + 7$
. $$\begin{array} { | c | c | } \hline x & y \\\hline - 4 & \\\hline - 2 & \\\hline 2 & \\\hline 3 & \\\hline 5 & \\\hline\end{array}$$

Question 5

If $M ( 2,3 )$
is the midpoint of the line segment AB, and if A has coordinates $( 6,8 )$
find the coordinates of B.

Question 6

Write the equation for the line passing through the point (8, -11) and parallel to the line x + 2y = 8.

Question 7

Write an equation for the line with a slope of 2 and y-intercept of -1.

Question 8

Find an equation of the circle that has the points P(5, 8) and Q(9, -6) as the endpoints of a diameter.

Question 9

Write an equation for the line with an x-intercept of -4 and y-intercept of 16.

Question 10

Complete the table below by determining both the slope and the y-intercept of each of the lines. $$\begin{array} { | c | c | c | } \hline \text { equation of the line } & \text { slope } & y \text {-intercept } \\\hline x + y = 2 & & \\\hline 2 x + y = 4 & & \\\hline 3 y + 6 = 0 & & \\\hline 4 x - 2 y = 0 & & \\\hline\end{array}$$

Question 11

Fill in the table of values for the function $y = \sqrt { x } / 5$
. $$\begin{array} { | c | c | } \hline x & y \\\hline 0 & \\\hline 25 & \\\hline 225 & \\\hline 625 & \\\hline 900 & \\\hline\end{array}$$

Question 12

Find the equation of the circle with radius 4 and center (-2, -3).

Question 13

Find the midpoint of the line segment joining the points $( 3,1 )$
and $( 2,5 )$

Question 14

Which of the points A(6, 7) or B(5, 8) is closer to the origin?

Question 15

Fill in the table of values for the function $$x y = 7$$
. $$\begin{array} { l l l l l l } x & 4 & - 1 & 2 & 4 & 7 \\y & & & & &\end{array}$$

Question 16

Write the equation for the line passing through the point (15, 17) which is perpendicular to the line y = 7.

Question 17

Do the graphs intersect in the given viewing rectangle? If they do, how many points of intersection are there?

Question 18

If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation
Suppose the dosage for an adult is 300 mg
a) Find the slope. What does it represent?
b) What is the dosage for a newborn?

Question 19

Write an equation for the line passing through the point (-1, 2) and the point (3, -4).

Question 20

Find the x and y-intercepts of the graph of the equation
.

Question 21

The graph shows the pressure experienced by an ocean diver at two different depths. Find and interpret the midpoint of the line segment shown in the graph.

Question 22

Write an equation that expresses y as it varies inversely as G.

Question 23

The cost C of printing a magazine is jointly proportional to the number of pages p in the magazine and the number of magazines printed m
a)Write an equation that expresses this joint variation
b)Find the constant of proportionality if the printing cost is $120,000 for 4000 copies of a 120-page magazine
c)How much would the printing cost be for 2500 copies of an 85-page magazine?

Question 24

Write an equation that expresses the statement.D is proportional to the square root of x.

Question 25

Express the statement as a formula.M varies directly as x and inversely as y
Use the information that if x = 24 and y = -4 then M = 36 to find the constant of proportionality.

Question 26

If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation
Suppose the dosage for an adult is 400 mg
a) Find the slope. What does it represent?
b) What is the dosage for a newborn?

Question 27

Express the statement as a formula.

Question 28

Fill in the table of values for the function $y = | x - 6 |$
$$\begin{array} { | c | c | } \hline x & y \\\hline 4 & \\\hline - 1 & \\\hline 2 & \\\hline 3 & \\\hline 5 & \\\hline\end{array}$$

Question 29

Fill in the table of values for the function $y = \frac { \sqrt { x } } { 5 }$
. $$\begin{array} { | c | c | } \hline x & y \\\hline 0 & \\\hline 25 & \\\hline 225 & \\\hline 625 & \\\hline 900 & \\\hline\end{array}$$

Question 30

Write an equation for the line passing through the point (-1,2) and the point (3,-4).

Question 31

Write an equation that expresses the statement.y varies inversely as G.

Question 32

Find the equation of the circle with radius 4 and center (2, 3).

Question 33

The relationship between the Fahrenheit (F) and Celsius
c) temperature scales is given by the equation $F = \frac { 9 } { 5 } C + 32$
Complete the following table to compare the two scales at the given values. $$\begin{array} { | c | c | } \hline C & F \\\hline - 25 & \\\hline - 15 & \\\hline - 35 & \\\hline & 86 \\\hline & 104 \\\hline & 77 \\\hline\end{array}$$

Question 34

Write the equation for the line passing through the point (8,-11) and parallel to the line x + 2y = 8.

Question 35

Write an equation for the line through the point (2,18) which has a slope of 5.

Question 36

Determine which point A(2, 3) or B(1, 4) is closer to the origin?

A) Point A(2, 3) is closer to the origin
B) Point B(1, 4) is closer to the origin.

Question 37

\
Find the approximate solution(s) of the equation
in the interval
by drawing a graph in an appropriate viewing rectangle. State each answer correct to two decimals.

Question 38

Find the midpoint of the segment joining the points (7, -6) and (15, -2)

A) (-8, -4)
B) (-4, -11)
C) (-4, 22)
D) (11, -4)
E) (22, -8)

Question 39

Find the distance between the points (2,2) and (5,6).

Question 40

Write the equation for the line passing through the point (15,17) which is perpendicular to the line y = 7.

Question 41

Determine the sketch of the region given by the set.

Question 42

Determine which point is on the graph of the equation y = 5x + 6

A) ( -7, -16 )
B) ( -5, -14 )
C) ( 5, 6 )
D) ( -4, -14 )
E) ( -4, -15 )

Question 43

Find an equation of the circle with the center at (-5, 1) and the radius of 1.

Question 44

Find the center and radius of the circle. $$x ^ { 2 } - x + \frac { 5 } { 4 } + y ^ { 2 } - 2 y = \frac { 1 } { 4 }$$

Question 45

Question 46

Write an equation that expresses that R is proportional to the square root of y.

Question 47

Find the x- and y-intercepts of the graph of the equation.

Question 48

Test the equation for symmetry.

Question 49

The loudness L of a sound (measured in decibels, dB) is inversely proportional to the square of the distance d from the source of the sound. A person who is 10 ft from a lawn mower experiences a sound level of 70 dB. How loud is the lawn mower when the person is 25 ft away?

Question 50

Calculate the y-coordinates in the table below for the function $$y = 3 x ^ { 2 } + 7$$
$$\begin{array} { | c | c | } \hline x & y \\\hline - 4 & \\\hline - 2 & \\\hline 2 & \\\hline 3 & \\\hline 5 & \\\hline\end{array}$$

Question 51

Do the graphs intersect in the given viewing rectangle? If they do, how many points of intersection are there?

Question 52

If M(3, 4) is the midpoint of the line segment AB, and if A has coordinates (1, 2), find the coordinates of B

A) (-3, -5)
B) (-5, 6)
C) (-5, -4)
D) (5, 6)
E) (5, -6)

Question 53

Question 54

Determine the correct equation for the line passing through the point (5, 16) and the point (17, 3).

Question 55

Express the statement as a formula.

Question 56

Determine the equation that expresses the statement.

Question 57

Determine the correct equation for the line passing through the point (2, 22) with a slope of 7.

Question 58

Find the center and radius of the circle.

Question 59

 

Question 60

Express the statement M varies directly as x and inversely as y as a formula.Use the information that if x = -20 and y = 4 then M = -25 to find the constant of proportionality

A) 9
B) 5
C) 15
D) 7
E) 6

Question 61

Draw the graph.

Question 62

Question 63

If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation Suppose the dosage for an adult is 300 mg. Find the dosage for a newborn

A) 299 mg
B) 4.17 mg
C) 15 mg
D) 150 mg
E) none of these

Question 64

Determine which point is on the graph of the equation y = 5x + 6.

Question 65

Draw the graph.

Question 66

Find the slope and y-intercept for the line x + y = 7 and draw its graph.

Question 67

Determine the equation that expresses B is proportional to R and inversely proportional to t.Symbols a, b, and c are constants.

Question 68

 

Question 69

A car is traveling on a curve that forms a circular arc. The force needed to keep the car from skidding is jointly proportional to the weight
Of the car and the square of its speed s, and is inversely proportional to the radius r of the curve. A car weighing 2,500 lbs travels around a curve at 70 mi/h. The next car to round this curve weighs 4,900 lbs and requires the same force as the first car to keep from skidding. How fast is the second car traveling?

A) 49 mi/h
B) 50 mi/h
C) 44 mi/h
D) 54 mi/h
E) 52 mi/h

Question 70

Draw the graph.

Question 71

Determine which point A(2, 3) or B(1, 4) is closer to the origin?

Question 72

Draw the graph.

Question 73

If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation Suppose the dosage for an adult is 300 mg. Find the dosage for a newborn.

Question 74

Determine the correct equation for the line passing through the point (2,22) with a slope of 7.

Question 75

Find the slope of the line through P(5,-5) and Q(-8,34).

Question 76

A car is traveling on a curve that forms a circular arc. The force needed to keep the car from skidding is jointly proportional to the weight
Of the car and the square of its speed s, and is inversely proportional to the radius r of the curve. A car weighing 2,500 lbs travels around a curve at 70 mi/h. The next car to round this curve weighs 4,900 lbs and requires the same force as the first car to keep from skidding. How fast is the second car traveling?

Question 77

Determine the correct equation for the line passing through the point (5,16) and the point (17,3).

Question 78

Test the equation for symmetry.

Question 79

Find the slope and y-intercept for the line x + y = 7 and draw its graph.

Question 80

Solve the equation graphically in the interval