Question

determine the graph of the function ( y = 4^{x + 2} ).

Explanation:

Step1: Analyze the function \(y = 4^{x+2}\)

We know that the general form of an exponential function is \(y=a^{x + h}+k\). For \(y = 4^{x+2}\), when \(x=-2\), \(y = 4^{-2 + 2}=4^{0}=1\).

Step2: Check the behavior as \(x\to\infty\) and \(x\to-\infty\)

As \(x\to\infty\), \(y = 4^{x+2}\to\infty\) (since the base \(a = 4>1\)). As \(x\to-\infty\), \(y = 4^{x+2}\to0\) (because \(y=a^{x}\), \(a>1\), \(\lim_{x\to-\infty}a^{x}=0\)).

Answer:

Assuming option \(a\) has the correct \(y\) - intercept behavior (passing through \((- 2,1)\) and increasing as \(x\) increases and approaching \(0\) as \(x\to-\infty\)), the answer is \(a\).