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Directions: Rewrite each of the following exponential functions in the equivalent general form y = ab^x,...

Directions: Rewrite each of the following exponential functions in the equivalent general form y = ab^x, where a and b are positive constants.
1. f(x) = 7x+2
2. g(x) = 5x−1
3. h(x) = 2x+3
4. k(x) = 3x−3
5. p(x) = 2(4)x−1
6. m(x) = 3x
7. r(x) = 4√x
8. n(x) = 8√3
9. s(x) = 5(2)3x
10. Which of the following functions is an equivalent form of the function f(x) = 4 · 36x?
(A) f(x) = 2 · 6(1/2)x
(B) f(x) = 2 · 6x
(C) f(x) = 4 · 6(1/2)x
(D) f(x) = 4 · 6x
11. Which of the following functions is an equivalent form of the function g(x) = 5 · 32x?
(A) g(x) = 45x
(B) g(x) = 5 · 9x
(C) g(x) = 25 · 3x
(D) g(x) = 25 · 9x

Answer

  1. f(x) = 7x+2: y = 7 · 7^x

  2. g(x) = 5x−1: y = 5 · 5^x

  3. h(x) = 2x+3: y = 2 · 2^x

  4. k(x) = 3x−3: y = 3 · 3^x

  5. p(x) = 2(4)x−1: y = 2 · 4^x

  6. m(x) = 3x: y = 3 · 3^x

  7. r(x) = 4√x: y = 4^(1/2) · 4^x

  8. n(x) = 8√3: y = 8^(1/3) · 8^x

  9. s(x) = 5(2)3x: y = 5 · (2^3)^x

  10. 10. The equivalent form of f(x) = 4 · 36^x is (D) f(x) = 4 · 6^x.

  11. 11. The equivalent form of g(x) = 5 · 32^x is (B) g(x) = 5 · 9^x.

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