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 f…

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asked May 5, 2021 144k views

2 Answers

Mnemenaut · Answer 1 · 2021-05-08T17:03:12+0000

Answer:

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

Explanation:

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