Question

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 function g? Replace the values of a and k in the function equation. G(x)=6^ax +k

Answer 1

Answer: 1/5 and 8

Explanation:

Answer 2

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

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`