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swat32
3 years ago
13

The function f(x) = 6x + 8 is transformed to function g through a horizontal stretch by a factor of 5. What is the equation of f

unction g? Replace the values of a and k in the function equation. G(x)=6^ax +k
Mathematics
1 answer:
elixir [45]3 years ago
6 0

Answer:

g(x) = 30\cdot x +40; a \approx 1.898, k = 40.

Step-by-step explanation:

The resultant function is obtained by multiplying f(x) by a real number k. That is:

g(x) = k \cdot f (x)

If k = 5 and f(x) = 6\cdot x + 8, then g(x) is:

g(x) = 5\cdot (6\cdot x + 8)

g(x) = 30\cdot x +40

Given that presence of the expression g(x) = 6^{a}\cdot x + k, then:

6^{a} = 30 and k = 40

The value of a is obtained by applying the definition of logarithms:

a = \log_{6}30

a \approx 1.898

Finally, the value of k is found by direct comparison:

k = 40

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