Domain and Range of Reciprocal Functions Solutions

• When writing the domain and range for reciprocal functions, use    set-builder    notation.
• This math shorthand allows you to    define the sets    of numbers, rather than listing all of the values.

Symbol	Read as	Meaning
{ }	set brackets, “the set of …”	a group or set
|	“such that”
∈	“an element of”	is part of a set
/	“is not” (i.e. ≠: “is not equal to,”$\notin :$ “is not an element of”)	symbol to show negation
ℕ, 𝕎, ℤ, ℚ, 𝕀, ℝ	Possible sets of numbers

• Here are some examples using set-builder notation:
  • “The set of all x’s such that x is an element of the Real number and cannot equal 2” $\underline{ \left\{x\right|x\in \mathrm{ℝ},x\ne 2\} }$
  • “The set of all q’s such that q is an element of the Natural numbers, and between 2 and 8” This could also be written as {3, 4, 5, 6, 7} $\underline{ \left\{q\right|q\in \mathrm{\mathbb{N}},2<q<8\} }$

Note

Set-builder notation is used here. Interval notation will also be used later in this level. See Algebra 1: Principles of Secondary Mathematics for more on interval notation.

• The domain is the set of     x-values    for a function.

• The range is the set of     y-values    for a function.

• For reciprocal functions, use the    asymptotes    to help determine restrictions for the domain and range.

• Graphs do not cross vertical asymptotes because this would make the denominator    undefined   .

• Vertical asymptotes are boundaries for the    hyperbola   .

• Horizontal asymptotes show the end behavior of a hyperbola as the graph moves toward    infinity   .

Note

End behavior will be discussed in more detail in later lessons and levels.

Example 4

Name the domain and range of the reciprocal function.

Note

Recall that y and f (x) can be used interchangeably. Since the function is given as f (x), it is used for the range.

Example 5

Name the domain and range of the reciprocal function.