identify the graph for the equation. \n$y = 3(3)^x$

Explanation:

Step1: Find y-intercept (x=0)

Substitute $x=0$ into $y=3(3)^x$: $y=3(3)^0 = 3(1) = 3$ So the graph passes through $(0, 3)$.

Step2: Test positive x value (x=1)

Substitute $x=1$ into $y=3(3)^x$: $y=3(3)^1 = 3(3) = 9$ So the graph passes through $(1, 9)$.

Step3: Test negative x value (x=-1)

Substitute $x=-1$ into $y=3(3)^x$: $y=3(3)^{-1} = 3\times\frac{1}{3} = 1$ So the graph passes through $(-1, 1)$.

Step4: Match points to graphs

The first graph passes through $(0,3)$, rises rapidly for positive $x$, and approaches 0 for negative $x$, matching our calculated points. The second graph has a y-intercept at 0 (incorrect), and the third graph decreases as $x$ increases (exponential decay, not growth).

Answer:

The first graph (leftmost graph, passing through (0,3), rising steeply for positive x, approaching 0 for negative x)