Relation
A relation is a set of ordered numbers, or a comparison of two things.
Examples:
a set of ordered pairs: { (4, 2), (-5, 7), (-2, 8), (4, 8) }
a list of students and their grades: { (Adam, 85), (Becky, 90), (Charles, 95), (Doug, 90), (Ellen, 85) }
The domain is all the x-values. The range is all the y-values. When listing the domain or range, list each number only once, and list them in order from least to greatest.
Examples:
a set of ordered pairs: { (4, 2), (-5, 7), (-2, 8), (4, 8) }
a list of students and their grades: { (Adam, 85), (Becky, 90), (Charles, 95), (Doug, 90), (Ellen, 85) }
The domain is all the x-values. The range is all the y-values. When listing the domain or range, list each number only once, and list them in order from least to greatest.
Functions
A function is a relation that has exactly one y-value for each x-value.
The relation { (4, 2), (-5, 7), (-2, 8), (4, 8) } IS NOT a function, because the x-value 4 has two y-values: 2 and 8.
The relation { (Adam, 85), (Becky, 90), (Charles, 95), (Doug, 90), (Ellen, 85) } IS a function, since every x-value (the student) has only one y-value (the grade). It's ok that the y-values are used more than once.
Scroll through the document below to see the 5 ways to show a function.
The relation { (4, 2), (-5, 7), (-2, 8), (4, 8) } IS NOT a function, because the x-value 4 has two y-values: 2 and 8.
The relation { (Adam, 85), (Becky, 90), (Charles, 95), (Doug, 90), (Ellen, 85) } IS a function, since every x-value (the student) has only one y-value (the grade). It's ok that the y-values are used more than once.
Scroll through the document below to see the 5 ways to show a function.
Sequences
An arithmetic sequence is a sequence of numbers that increase of decrease at a constant rate of addition.
Example: 4, 7, 10, 13, 16, ...
The common difference (d) is the amount that is added on to each term to form the next term.
In the example, the common different is 3. (d = 3)
A geometric sequence is a sequence formed by multiplying the same number to each term.
Example: 2, 4, 8, 16, 32, 64, ...
The common ratio (r) is the amount that is multiplies to each term to produce the next term.
In the example, the common ratio is 2. (r = 2)
Example: 4, 7, 10, 13, 16, ...
The common difference (d) is the amount that is added on to each term to form the next term.
In the example, the common different is 3. (d = 3)
A geometric sequence is a sequence formed by multiplying the same number to each term.
Example: 2, 4, 8, 16, 32, 64, ...
The common ratio (r) is the amount that is multiplies to each term to produce the next term.
In the example, the common ratio is 2. (r = 2)