Find the domain and graph the function.
-$F ( t ) = \frac { | t - 2 | } { t - 2 }$

A) D: $( - \infty , 0 ) \cup ( 0 , \infty )$
B) D: $( - \infty , 2 ) \cup ( 2 , \infty )$
C) D: $( - \infty , 2 ) \cup ( 2 , \infty )$
D) D: $( - \infty , \infty )$

Question

Find the domain and graph the function.
-$F ( t ) = \frac { | t - 2 | } { t - 2 }$

A) D: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B) D: $( - \infty , 2 ) \cup ( 2 , \infty )$ 
C) D: $( - \infty , 2 ) \cup ( 2 > , \infty )$ 
D) D: $( - \infty , \infty )$

Quizplus · Accepted Answer

The function is undefined at $t=2$ because it leads to division by zero. Thus, the domain of the function is $\mathbb{R} \setminus \{2\},$ which is equivalent to the given answer choice B. To graph this function, we can observe that it is equal to $-1$ when $t<2$ and $1$ when $t>2.$ However, at $t=2,$ the function is undefined, so we leave a hole in the graph at that point. Below is a rough sketch of the graph: [asy] unitsize(1.5 cm); draw((-3,-1)--(1.99,-1),red,Arrow(6)); draw((2.01,-1)--(3,-1),red,Arrow(6)); draw((-3,1)--(1.99,1),red,Arrow(6)); draw((2.01,1)--(3,1),red,Arrow(6)); draw((2,1)--(2,-1),dashed); label("$t < 2$", (-2, 0.5), red); label("$t > 2$", (2.5, 0.5), red); label("$F(t) = -1$", (-0.5, -1), red); label("$F(t) = 1$", (2.5, 1), red); label("2", (2, 0.2)); [/asy]

Find the Domain and Graph the Function F(t)=∣t−2∣t−2F ( t ) = \frac { | t - 2 | } { t - 2 }F(t)=t−2∣t−2∣​

Find the Domain and Graph the Function $F ( t ) = \frac { | t - 2 | } { t - 2 }$