What transformation change the graph of f(x) to the graph of g(x)? f(x)=x^2 g(x)=(x+3)^2-7

we are given

and

Transformation-1:

we can see that in place of x , we have x+3

whenever we have x+a

it means that function is shifted left side by 'a' units

so, in x+3 ,

f(x) is shifted to left side by 3 units

Transformation-2:

we can see that

y-value is subtracted by 7 units

whenever we have f(x)-a

it means that function is shifted downward  by 'a' units

f(x) is shifted to downward  by 7 units

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.