Question

what are the domain, range, and asymptote of \\(h(x) = 6^x - 4\\)?

domain: \\(\\{x \mid x \text{ is a real number}\\}\\); range: \\(\\{y \mid y > 4\\}\\); asymptote: \\(y = 4\\)
domain: \\(\\{x \mid x \text{ is a real number}\\}\\); range: \\(\\{y \mid y > -4\\}\\); asymptote: \\(y = -4\\)
domain: \\(\\{x \mid x > -4\\}\\); range: \\(\\{y \mid y \text{ is a real number}\\}\\); asymptote: \\(y = 4\\)
domain: \\(\\{x \mid x > 4\\}\\); range: \\(\\{y \mid y \text{ is a real number}\\}\\); asymptote: \\(y = -4\\)

Explanation:

Determine the domain of the exponential function

$$ \text{Domain} = \{x \mid x \text{ is a real number}\} $$

Determine the range of the exponential function

$$
LATEXBLOCK0
$$

Determine the horizontal asymptote

$$
LATEXBLOCK1
$$

Answer:

• domain: \(\{x \mid x \text{ is a real number}\}\); range: \(\{y \mid y > 4\}\); asymptote: \(y = 4\)
• domain: \(\{x \mid x \text{ is a real number}\}\); range: \(\{y \mid y > -4\}\); asymptote: \(y = -4\) (Correct answer)
• domain: \(\{x \mid x > -4\}\); range: \(\{y \mid y \text{ is a real number}\}\); asymptote: \(y = 4\)
• domain: \(\{x \mid x > 4\}\); range: \(\{y \mid y \text{ is a real number}\}\); asymptote: \(y = -4\)