Let f(x) = |x| / x , where x can be any real number except 0.
a. why is the number 0 excluded from the domain of f?

The number 0 is excluded from the domain of f(x) because f(x) is a rational function which is not defined if the denominator is zero.

Step-by-step explanation:

The Rational Function is defined as:

with Q(x) ≠ 0

Because a rational function is not defined when the denominator is zero.

In this case, Q(x) (the denomitador of the given function) is x. Therefore the domain of the given function is given by all real numbers except the restrictions of the function (where the function is not defined).

f(x) is not defined at x=0, that's why the zero is excluded.

actually your concept is wrong

step-by-step explanation:

150% of x =300

150x=300×100

x=(300×100)÷150

x=200

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.