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Murrr4er [49]
3 years ago
9

Item 5 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 th

e equation of g(x) g(x) ?
Mathematics
1 answer:
insens350 [35]3 years ago
8 0

Answer:

g(x)=4(3)^{x+1}+8

Step-by-step explanation:

Given:

The original function is given as:

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

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

According to the rule of function transformations, when the graph of a function is stretched in the vertical direction by a factor of 'C', where, 'C' is a number greater than 1, then the function rule is given as:

f(x)\to Cf(x)

Therefore, the function is multiplied by a factor of 'C' to get the equation of the stretched function.

Here, the the value of 'C' is 2. So, the equation of g(x) is given as:

g(x)=2f(x)\\g(x)=2[2(3)^{x+1}+4]\\g(x)=4(3)^{x+1}+8

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

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