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What is the horizontal asymptote of g(x) = -(2)^(x)?

1. What is the horizontal asymptote of g(x) = -(2)^(x)?
a. y = 2
b. y = 0
c. y = -1
d. x = 0
2. What transformation changes f(x) = 4^x into g(x) = (1/3)(4)^(x-2)?
a. Shift left 3 units
b. Vertical compression by a factor of 1/3
c. Vertical stretch by a factor of 3
d. Shift down 3 units
3. What is the horizontal asymptote of g(x) = 4^x - 6?
a. y = -6
b. y = 0
c. y = 4
d. x = -6

Answer

  1. b. y = 0 - The horizontal asymptote of an exponential function of the form g(x) = a(b)^x is y = 0 if there are no vertical shifts.

  2. b. Vertical compression by a factor of 1/3 - The transformation involves multiplying the function by 1/3, which is a vertical compression.

  3. a. y = -6 - The horizontal asymptote of g(x) = 4^x - 6 is y = -6 due to the vertical shift downward by 6 units.

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