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What is the vertical asymptote of h(x) = log8(x + 4) - 1?

1. What is the vertical asymptote of h(x) = log8(x + 4) - 1?
a. x = 4
b. x = -4
c. y = -1
d. x = 0
2. What is the domain of h(x) = log8(x + 4) - 1?
a. (4, ∞)
b. (-∞, ∞)
c. (-1, ∞)
d. (-4, ∞)
3. What is the x-intercept of the parent logarithmic function f(x) = log8(x)?
a. (0, 0)
b. (8, 0)
c. (1, 0)
d. (0, 1)

Answer

  1. Answer: b. x = -4

    Explanation: The vertical asymptote of a logarithmic function log_b(x + c) is x = -c. Here, c = 4, so the vertical asymptote is x = -4.

  2. Answer: d. (-4, ∞)

    Explanation: The domain of the function log8(x + 4) is x + 4 > 0, which simplifies to x > -4. Therefore, the domain is (-4, ∞).

  3. Answer: c. (1, 0)

    Explanation: The x-intercept of the parent logarithmic function f(x) = log_b(x) is (1, 0) because log_b(1) = 0 for any base b.

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