Question

PLEASE HELP!!

Let f(x)=2(3)^x+1 +4 .

The graph of f(x) is stretched vertically by a factor of 2 to form the graph of g(x) .

What is the equation of g(x) ?



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g(x) = ____


I would appreciate if you could also explain the solution and the answer as well ^^

Answer 1

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f(x) = 2(3)^{x+1} + 4

vertical stretch f(x) by a scale factor of a is a * f(x)

so yeah

g(x) = 2 * f(x)
$g(x) = 2 * (2(3)^{x+1} + 4)$
g(x) = 4(3)^(x+1) + 8 (distributed)

Answer 2

Answer:

The equation of g(x) is,  $4(3)^{x+1} +8$

Step-by-step explanation:

Given the function: $f(x) = 2(3)^{x+1} + 4$

Vertically stretch states that if y = f(x), then y =a f(x) gives a vertical stretch when a> 1.

It is given that the graph of f(x) is stretched vertically by a factor of 2 to form the graph of g(x)

then by definition of vertical stretch we have;

$g(x) = 2f(x)$         as 2> 1

Then, g(x) becomes = $2 (2(3)^{x+1} + 4)$ = $4(3)^{x+1} +8$

Therefore, the equation of g(x) is,  $4(3)^{x+1} +8$