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:

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

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:

$k = 40$