Question

which is the graph of \\(f(x) = 2(3)^x\\)?

Explanation:

Evaluate the y-intercept

Using the Y-Intercept and Exponential Functions knowledge points

$$ f(0) = 2(3)^0 = 2(1) = 2 $$

Evaluate the function at key points

Using the Function Evaluation knowledge point

$$
LATEXBLOCK0
$$

Match with the correct graph

Using the Graph Interpretation knowledge point

• The first graph has a y-intercept at \((0, 2)\) and passes through the point \((1, 6)\).
• The second graph passes through \((1, 9)\).
• The third graph passes through \((2, 8)\).
• The fourth graph shows a segment passing through \((2, 12)\).
• Therefore, the first graph represents \(f(x) = 2(3)^x\).

Answer:

• (A) The graph with y-intercept at \((0, 2)\) passing through the point \((1, 6)\) (Correct answer)
• (B) The graph passing through the point \((1, 9)\)
• (C) The graph passing through the point \((2, 8)\)
• (D) The graph passing through the point \((2, 12)\)