Question

how does the exponential function ( f(x)=2 cdot 3^{x}+4 ) appear as a graph?

Explanation:

Step1: Analyze the horizontal asymptote

For the exponential function \(y = a\cdot b^{x}+k\) (\(b> 1\)), the horizontal asymptote is \(y = k\). In the function \(f(x)=2\cdot3^{x}+4\), \(k = 4\). So the graph has a horizontal asymptote \(y = 4\).

Step2: Analyze the y - intercept

When \(x = 0\), \(f(0)=2\cdot3^{0}+4=2\times1 + 4=6\). So the graph passes through the point \((0,6)\).

Answer:

The graph with a horizontal asymptote \(y = 4\) and passing through \((0,6)\) (the upper graph in the given options).