All Algebra II Resources
Example Questions
Example Question #5 :Number Sets
If,, and, find the following set:
The union is the set that contains all of the numbers found in all three sets. Therefore the union is. You do not need to re-write the numbers that appear more than once.
Example Question #6 :Number Sets
If,, and, find the following set:
The intersection is the set that contains the numbers found in both sets. Therefore the intersection is.
Example Question #7 :Number Sets
Which set of numbers represents the union of E and F?
The union is the set of numbers that lie in set E or in set F.
.
In this problem set E contains terms, and set F contains terms. Therefore, the union of these two sets is.
Example Question #12 :How To Find The Domain Of A Function
Express the following in Set Builder Notation:
andstands for OR in Set Builder Notation
Example Question #81 :Number Theory
Find the intersection of the two sets:
To find the intersection of the two sets,,我们必须找到共同的元素由机器人h sets:
Example Question #82 :Number Theory
What type of numbers are contained in the set?
Natural
Irrational
Complex
Integers
Imaginary
Integers
We can use process of elimination to find the correct answer.
It can't beImaginarybecause we're not dividing by a negative number.
It can't beComplexbecause the number's aren't a mix of real and imaginary numbers.
It can't beIrrationalbecause they aren't fractions.
It can't beNaturalbecause there are negative numbers.
It must beIntegersthen! All the numbers are whole numbers that fit on the number line.
Example Question #83 :Number Theory
True or false:
The setcomprises only imaginary numbers.
True
False
False
Any even power of the imaginary unitis a real number. For example,
from the definition ofas the principal square root of.
Also, from the Power of a Power Property,
Example Question #12 :Number Sets
What is?
or A intersect B means what A and B have in common.
In this case both A and B have the numbers 1, 9, and 11.
Example Question #84 :Number Theory
True or false:
The following set comprises only imaginary numbers:
True
False
True
To raiseto the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the table below.
Every element in the setis equal toraised to an odd-numbered power, so when each exponent is divided by 4, the remainder will be either 1 or 3. Therefore, each element is equal to eitheror. Consequently, the set includes only imaginary numbers.
Example Question #19 :How To Find A Solution Set
Set A is composed of all multiples of 4 that are that are less than the square of 7. Set B includes all multiples of 6 that are greater than 0. How many numbers are found in both set A and set B?
Start by making a list of the multiples of 4 that are smaller than the square of 7. When 7 is squared, it equals 49; thus, we can compose the following list:
Next, make a list of all the multiples of 6 that are greater than 0. Since we are looking for shared multiples, stop after 48 because numbers greater than 48 will not be included in set A. The biggest multiple of 4 smaller that is less than 49 is 48; therefore, do not calculate multiples of 6 greater than 48.
Finally, count the number of multiples found in both sets. Both sets include the following numbers:
The correct answer is 4 numbers.
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