Find the domain and range of $f ( x ) = \frac { | x - 2 | } { x - 2 }$
A) Domain: $( - \infty , - 2 ) \cup ( - 2,2 ) \cup ( 2 , \infty )$ Range: $( - \infty , \infty )$
B) Domain: $( - \infty , \infty )$ Range: $( - \infty , \infty )$
C) Domain: $( - \infty , - 2 ) \cup ( - 2,2 ) \cup ( 2 , \infty )$ Range: $( - \infty , \infty )$
D) Domain: $( - \infty , - 2 ) \cup ( - 2,2 ) \cup ( 2 , \infty )$ Range: $\{ - 1,1 \}$

Question

Find the domain and range of $f ( x ) = \frac { | x - 2 | } { x - 2 }$
A) Domain: $( - \infty , - 2 ) \cup ( - 2,2 ) \cup ( 2 , \infty )$ Range: $( - \infty , \infty )$
B) Domain: $( - \infty , \infty )$ Range: $( - \infty  , \infty )$
C) Domain: $( - \infty , - 2 ) \cup ( - 2,2 ) \cup (  2 , \infty )$ Range: $( - \infty , \infty )$
D) Domain: $( - \infty , - 2 ) \cup ( - 2,2 ) \cup ( 2  , \infty )$ Range: $\{ - 1,1 \}$

Quizplus · Accepted Answer

The function is undefined at $x = 2$ because the denominator becomes zero, so the domain excludes 2. The function outputs either 1 or -1 depending on the sign of $x - 2$, hence the range is \{-1, 1\}.

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Find the Domain and Range Of $f ( x ) = \frac { | x - 2 | } { x - 2 }$