Answer:
The graph shifts 5 units left
Step-by-step explanation:
The given functions are;
f(x) = [tex]2^{x - 2}[/tex], g(x) = [tex]2^{x + 3}[/tex]
Therefore, we have;
When x = 2, f(2) = [tex]2^{2 - 2}[/tex] = 1 and g(2) = [tex]2^{2 + 3}[/tex] = 32
When x = 3, f(3) = [tex]2^{3 - 2}[/tex] = 2 and g(3) = [tex]2^{3 + 3}[/tex] = 64
When x = 6, f(6) = [tex]2^{6 - 2}[/tex] = 16 and g(6) = [tex]2^{6 + 3}[/tex] = 512
When x = 7, f(7) = [tex]2^{7 - 2}[/tex] = 32 and g(7) = [tex]2^{7 + 3}[/tex] = 1024
When x = 8, f(8) = [tex]2^{8 - 2}[/tex] = 64 and g(8) = [tex]2^{8 + 3}[/tex] = 2,048
Therefore, the y-value of f(x) obtained at x = 8, is obtained by g(x) at x = 3, and the graph is shifts(ed) 5 units left.
