Questions: Sketch the graph of f(x) = 2^(x+4).

Solution Steps

The function \(f(x) = 2^{x+4}\) is an exponential function. The base is 2, which is greater than 1, so the function will be increasing. The +4 in the exponent represents a horizontal shift to the left by 4 units.

When \(x = 0\), \(f(0) = 2^{0+4} = 2^4 = 16\). The graph should cross the y-axis at 16. Since the graphs only show up to 10 on the y-axis, look for a graph that appears to cross around 16 and is an increasing exponential function shifted left.

Exponential functions of this form do not cross the x-axis. We can check by setting \(0 = 2^{x+4}\), which has no solution.

Option A appears to be an increasing exponential that crosses the y-axis at 16 and has been shifted left. The other options do not meet the above criteria.

Final Answer