which is the graph of $f(x)=\frac{1}{4}(4)^x$?
which is the graph of $f(x)=\frac{1}{4}(4)^x$?
Answer
Explanation:
Step1: Find the y - intercept
Substitute (x = 0) into (y=\frac{1}{4}(4)^{x}). Then (y=\frac{1}{4}(4)^{0}=\frac{1}{4}\times1=\frac{1}{4}).
Step2: Check points
For (x = 1), (y=\frac{1}{4}(4)^{1}=\frac{1}{4}\times4 = 1). For (x = 2), (y=\frac{1}{4}(4)^{2}=\frac{1}{4}\times16 = 4).
We know that the general form of an exponential function is (y = ab^{x}), where (a=\frac{1}{4}) and (b = 4>1), so the function is an increasing exponential function.
The correct graph is the one where when (x = 0,y=\frac{1}{4}), when (x = 1,y = 1) and when (x=2,y = 4).
Answer:
The graph with points ((0,\frac{1}{4})), ((1,1)) and ((2,4)) (assuming one of the given graphs has these points and is an increasing exponential - type graph).