Transformation involves changing the position of a graph
The equation of g(x) is [tex]\mathbf{g(x) = 8(2)^x}[/tex]
A geometric function is represented as:
[tex]\mathbf{y =ab^x}[/tex]
The graph of g(x) passes through (-1,4) and (-2,2)
So, we have:
[tex]\mathbf{2 =ab^{-2}}[/tex]
[tex]\mathbf{4 =ab^{-1}}[/tex]
Divide both equations
[tex]\mathbf{\frac{4}{2} =\frac{ab^{-1}}{ab^{-2}}}[/tex]
Divide
[tex]\mathbf{2 =b}[/tex]
Rewrite as:
[tex]\mathbf{b =2}[/tex]
Substitute 2 for b in [tex]\mathbf{4 =ab^{-1}}[/tex]
[tex]\mathbf{4 = a2^{-1}}[/tex]
Multiply both sides by 2
[tex]\mathbf{8 = a}[/tex]
Rewrite as:
[tex]\mathbf{a = 8}[/tex]
Substitute 2 for b and 8 for a in [tex]\mathbf{y =ab^x}[/tex]
[tex]\mathbf{y = 8(2)^x}[/tex]
Express as a function
[tex]\mathbf{g(x) = 8(2)^x}[/tex]
Hence, the equation of g(x) is [tex]\mathbf{g(x) = 8(2)^x}[/tex]
Read more about function transformation at:
https://brainly.com/question/13810353
