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