Question

I don't understand please explain in simple words the transformation that is happening

Answer 1

if we want to get g(x) = 2(5)^x + 1 from f(x) = 5^x, this is what we need to do:

f(x) = 5^x

1. Multiply f(x) by 2, then we get 2(5)^x

2. Add 1, then we get 2(5)^x + 1

and this is g(x)

Function Notation......................Words

2 f(x) = 2(5)^x ......................Scale f(x) by two or multiply f(x) by 2

2 f(x) + 1 = 2(5)^x + 1 ................Shift 2f(x) by one up or add 1 to 2f(x)

2(5)^x + 1 ...................... We get g(x) = 2(5)^x + 1