Which of the following rational functions could represent the graph shown?

Options

A. `r(x)=3`
B. `r(x)=(x-3)/(x-2)`
C. `r(x)=(2)/(x-3)`
D. `r(x)=(3x-6)/(x-2)`

Answer

D

Explanation

Difficult: Easy
Category: Passport to Advanced Math/ Exponents
Strategic advice: When matching a graph to an equation, look for key freatures for the graph, particularly when there is a feature that stands out.
Getting to the Answer: There is a "hole" in this graph (the open dot), which means that the function is not defined at perticular value of x, in this cause x=2 ( the x-coordinate of the open dot). Thnk about what could cause that. A denominator that equals 0 when x=2 is the correct choices-you can eliminate A(because there is no denominaton), and you can eliminate C not x=2). To choose between B and (D), simplify the functions to see which results in a horizontal line at r(x)=3 (because the line is at y=3). The function in B doesn't simplify at all skip it for now. For (D):
`r(x)=(3x-6)/(x-2)`
`r(x)=(3(x-2))/(x-2)`
`r(x)=3`
The equation in (D) is indeed a horizontal line at y=3 with a "hole" at x=2.