To which subsets of the real numbers does 2 radical 2 belong?
(a) natural
b) whole
c) irrational
d) integers
e) rational

is irrational .

Step-by-step explanation:

The Natural numbers are {1,2,3,4,5,6,7,....}.

Natural numbers are also called counting numbers because they are numbers people use to count with.

Whole numbers are almost the same as natural numbers.  They include one extra number which is 0.

So the whole numbers are {0,1,2,3,4,5,6,7,...}.

Irrational numbers are real numbers that aren't rational numbers.

Rational numbers are number that can be written as fractions where the numerator and denominator are integers (bottom integer is not 0).

Terminating decimals, repeating decimals, and integers all can be written this way which makes them rational.

Integers are numbers in the set {...,-4,-3,-2,-1,0,1,2,3,4,...}.  So these are your counting numbers, 0, and the opposite of your counting numbers.

You want to figure out which set does belong to.

You cannot simplify this number anymore than it is. So this is definitely not a number you can count to. It is not the opposite of a counting number.  It is also not 0.  We have ruled out the following sets: Natural, whole, and integers.

So it is between rational and irrational.

.

.

2 is not a perfect square.

So

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.