What is the domain of the relation {(3, 4), (4, 3), (4, 4), (5, 2)}?

a) {2, 3, 4, 5}
b) {3, 4, 5}
c) {4}
d) {2, 3, 4}

B) {3, 4, 5}

Step-by-step explanation:

Domain: All values that can go into a function or a relation as input are called domain. When we enter these values into a function we get range of the function.

Therefore if we write the relation in the ordered pair form of (x,y) all x values are domain.

In the given relation {(3, 4), (4, 3), (4, 4), (5, 2)}, 4 appears twice but we will write it only once because of the definition of function i.e. function is a process or a relation that associates each element x of a set X, the domain of the function, to a single element y of another set Y

Choice B is correct answer.

Step-by-step explanation:

We have given a relation.

{(3, 4), (4, 3), (4, 4), (5, 2)}

We have to find the domain of above relation.

If f is a function from X to Y then X is called the domain of f and Y is called range of f.

Domain is defined as the input of function.

Hence, the input values of given function is:

3,4,4,5

Now, dom f  = {3,4,5} which is the answer.

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24