Question

drag the key features to the correct location on the image. each key feature can be used more than once, but not all key features will be used.

which key features are present in these three functions?

\\f(x) = \frac{-2x + 4}{x - 6}\\
\\g(x) = \frac{x^2 - 2x}{x^2 + x - 6}\\
\\h(x) = \frac{x^2 - 2x}{x - 6}\\

options:

• domain: \\((-\infty, 2) \cup (2, 6) \cup (6, \infty)\\)
• horizontal asymptote: \\(y = -2\\)
• domain: \\((-\infty, 6) \cup (6, \infty)\\)
• oblique asymptote
• domain: \\((-\infty, -3) \cup (-3, 2) \cup (2, \infty)\\)
• domain: \\((-\infty, -3) \cup (-3, \infty)\\)
• domain: \\((-\infty, -3) \cup (-3, 6) \cup (6, \infty)\\)
• horizontal asymptote: \\(y = 1\\)

Explanation:

Analyze \(f(x) = \frac{-2x + 4}{x - 6}\)

$$
LATEXBLOCK0
$$

Analyze \(g(x) = \frac{x^2 - 2x}{x^2 + x - 6}\)

$$
LATEXBLOCK1
$$

Analyze \(h(x) = \frac{x^2 - 2x}{x - 6}\)

$$
LATEXBLOCK2
$$

Answer:

\(f(x) = \frac{-2x + 4}{x - 6}\)	\(g(x) = \frac{x^2 - 2x}{x^2 + x - 6}\)	\(h(x) = \frac{x^2 - 2x}{x - 6}\)
horizontal asymptote: \(y = -2\)	horizontal asymptote: \(y = 1\)	oblique asymptote