Answer:
[tex]g(x)=4(3)^{\left(x+1\right)}+8[/tex]
Step-by-step explanation:
Given equation is:
[tex]f(x)=2(3)^{\left(x+1\right)}+4[/tex]
Now it says that graph of f(x) is stretched vertically by a factor of 2 to form the graph of g(x).
Now we need to find about what is the equation of g(x).
We know that if function f(x) is stretched vertically by a factor of "a" then we get a*f(x)
Here factor is 2
So we just need to multiply g(x) with 2.
g(x)=a*f(x)
g(x)=2*f(x)
[tex]g(x)=2\left(2(3)^{\left(x+1\right)}+4\right)[/tex]
[tex]g(x)=4(3)^{\left(x+1\right)}+8[/tex]
Hence final answer is:
[tex]g(x)=4(3)^{\left(x+1\right)}+8[/tex]
Answer:
The equation of g(x) is:
[tex]g(x)=4\times 3^{x+1}+8[/tex]
Step-by-step explanation:
We are given a function f(x) as:
[tex]f(x)=2\times 3^{x+1}+4[/tex]
now we are given a condition that the graph of f(x) is stretched vertically by a factor of 2 to form the graph of g(x).
Now we know that for any initial function f(x) if the function is stretched vertically by a factor "a" to form the other function g(x) then the equation of the resultant function is given by:
[tex]g(x)=a f(x)[/tex]
now here [tex]a=2[/tex]
and [tex]f(x)=2\times 3^{x+1}+4[/tex]
Hence, the resultant function g(x) is given by:
[tex]g(x)=2\times (2\times 3^{x+1}+4)[/tex]
[tex]g(x)=4\times 3^{x+1}+8[/tex]
Hence, the equation of g(x) is:
[tex]g(x)=4\times 3^{x+1}+8[/tex].
