Question

consider the following function:

\\f(x) = \frac{2x}{3x^2 - 3}\\

what is the domain of the function?
all real numbers except -1 and 1

which of the following describes the end behavior of \\f(x) = \frac{2x}{3x^2 - 3}\\?

• the graph approaches 0 as x approaches infinity.
• the graph approaches 0 as x approaches negative infinity.
• the graph approaches 2/3 as x approaches infinity.
• the graph approaches -1 as x approaches negative infinity.

Explanation:

Identify the degrees of numerator and denominator

Using the Rational Functions knowledge point

$$
LATEXBLOCK0
$$

Determine the horizontal asymptote

Using the Horizontal Asymptotes knowledge point

$$
LATEXBLOCK1
$$

Evaluate the given options

Using the Horizontal Asymptotes knowledge point

$$
LATEXBLOCK2
$$

Answer:

• The graph approaches 0 as x approaches infinity. (Correct answer)
• The graph approaches 0 as x approaches negative infinity. (Correct answer)
• The graph approaches 2/3 as x approaches infinity.
• The graph approaches -1 as x approaches negative infinity.