Question

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)g(x) ?

Answer 1

If f is strectced vertically by a factor of 2 to form g(x) then the eqn takes the form g(x) = 2 f(x). Here f(x) = 2(3)^( x + 1) + 4. This gives us 2(2(3)^(x +1) + 4). So we have g(x) = 4(3)^(x + 1) + 8. g(x)g(x) = (4(3) ^(x +1) + 8) * (4(3)^(x+1) +8). This gives us 16(3)^2(x + 1) + 32(3)^(x +1) + 32(3)^(x +1) + 16(3)^2(x +1). Then we have 16(3)^(2x + 2) + 64(3)^(x +1) + 16(3)^(2x+2). So our final answer is 32(3)^(2x +2) + 64(3)^(x + 1)