Mathematical Vocabulary:
Word
Domain
Translation
All the possible inputs or x-values for
a function
3
𝑓(𝑥) = 𝑥
Domain (x)
Range(y)
2
8
10
1000
-1
-1
Example
What are the domains for these functions?
1) √𝑥 − 1 – D:
2) √𝑥 -- D:
3) 𝑥 2 – D:
4) 𝑥 3 – D:
Range
D: {-1, 2, 10}
All the possible outputs or y-values
for a function.
𝑓(𝑥) = 𝑥 3
Domain (x)
Range(y)
2
8
10
1000
-1
-1
What are the ranges for these functions?
5) √𝑥 − 1 – R:
6) √𝑥 -- R:
7) 𝑥 2 – R:
8) 𝑥 3 – R:
< 𝑜𝑟 ≤
This is the symbol that represents
“less than (<)” or “less than or equal
to (≤).”
What are the possible values for the following
inequalities?
9) 𝑥 + 1 < 2
The symbol < means that the number
you pick has to be strictly less than
than the number it is comparing to;
for example: 𝑥 < 4 means we can
pick numbers from negative infinity to
3.9999999999….
The symbol ≤ means that the number
you pick can be less than or equal to
the number it is comparing to; for
example: 𝑥 ≤ 4 means we can pick
numbers from negative infinity to 4.
10) 𝑥 ≤ 20
11) −2 > 𝑥
12) 𝑥 2 + 2𝑥 + 2 ≤ 10
13) √𝑥 < 18
> 𝑜𝑟 ≥
This is the symbol that represents
“greater than (>) or “greater than or
equal to (≥). "
What are the possible values for the following
inequalities?
14) 𝑥 + 1 > 2
The symbol > means that the number
you pick has to be strictly greater
than the number it is comparing to;
for example: 𝑥 > 4 means we can
pick numbers from 4.0000001 to
positive infinity.
The symbol ≥ means that the number
you pick can be greater than or equal
to the number it is comparing to; for
example: 𝑥 ≥ 4 means we can pick
numbers from 4 to positive infinity.
15) 𝑥 ≥ 20
16) −2 < 𝑥
17) 𝑥 2 + 2𝑥 + 2 ≥ 10
18) √𝑥 > 18
Inverse
The inverse means we have to find
the operations that “undo” or
“reverse” the original function’s
operations. The inverse is often
denote 𝑓 −1 (𝑥).
Write in English and math what the reverse
operations are:
19) 𝑓(𝑥) = 𝑥 2
Example:
𝑓(𝑥) = 2𝑥 + 1
20) 𝑓(𝑥) = 2𝑥 2 − 2
The inverse is
𝑓 −1 (𝑥) =
𝑥−1
2
to write this in English:
21) 𝑓(𝑥) = √𝑥 − 1 + 2
we subtract one (the inverse of
adding by 1) from both sides and then
divide by two (the inverse of
multiplying by 2)
22) 𝑓(𝑥) = 2√2𝑥 + 1