Question

which exponential function is represented by the graph?

\\(f(x) = 2(3^x)\\)
\\(f(x) = 3(3^x)\\)
\\(f(x) = 3(2^x)\\)
\\(f(x) = 2(2^x)\\)

Explanation:

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<reasoning>

Identify the y-intercept

Using the Y-Intercept knowledge point
\[

$$\begin{aligned} &f(0) = 3\\ &f(x) = a \cdot b^x \implies a \cdot b^0 = a \implies a = 3 \end{aligned}$$

\]

Determine the base of the function

Using the Exponential Functions knowledge point
\[

$$\begin{aligned} &f(1) = 6\\ &3 \cdot b^1 = 6 \implies b = 2\\ &f(x) = 3(2^x) \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(f(x) = 2(3^x)\)</mcq-option>
<mcq-option>(B) \(f(x) = 3(3^x)\)</mcq-option>
<mcq-correct>(C) \(f(x) = 3(2^x)\)</mcq-correct>
<mcq-option>(D) \(f(x) = 2(2^x)\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the y-intercept

Using the Y-Intercept knowledge point
\[

$$\begin{aligned} &f(0) = 3\\ &f(x) = a \cdot b^x \implies a \cdot b^0 = a \implies a = 3 \end{aligned}$$

\]

Determine the base of the function

Using the Exponential Functions knowledge point
\[

$$\begin{aligned} &f(1) = 6\\ &3 \cdot b^1 = 6 \implies b = 2\\ &f(x) = 3(2^x) \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(f(x) = 2(3^x)\)</mcq-option>
<mcq-option>(B) \(f(x) = 3(3^x)\)</mcq-option>
<mcq-correct>(C) \(f(x) = 3(2^x)\)</mcq-correct>
<mcq-option>(D) \(f(x) = 2(2^x)\)</mcq-option>
</answer>

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