which graph is the sequence defined by the function $f(x) = 3(2)^{x - 1}$?

Explanation:

Step1: Calculate f(1)

$f(1)=3(2)^{1-1}=3(2)^0=3\times1=3$

Step2: Calculate f(2)

$f(2)=3(2)^{2-1}=3(2)^1=3\times2=6$

Step3: Calculate f(3)

$f(3)=3(2)^{3-1}=3(2)^2=3\times4=12$

Step4: Calculate f(4)

$f(4)=3(2)^{4-1}=3(2)^3=3\times8=24$

Step5: Calculate f(5)

$f(5)=3(2)^{5-1}=3(2)^4=3\times16=48$

Step6: Match points to graphs

The points are $(1,3), (2,6), (3,12), (4,24), (5,48)$, which matches the middle graph.

Answer:

The middle graph (with points (0,3), (1,6), (2,12), (3,24), (4,48), (5,96) — note: the sequence uses positive integer x-values starting at 1, so the relevant points are (1,6), (2,12), (3,24), (4,48), (5,96) which align with the function's outputs)