Fourth graph
Step-by-step explanation:
First: some important housekeeping:
Please use " ^ " to denote exponentiation: f(x) = (1/4)(4)^x, and enclose fractional coefficients such as 1/4 inside parentheses: (1/4).
f(x) = (1/4)(4)^x is an exponential growth function; we know that because the base is greater than 1. The graph is vertically compressed by a factor of 1/4.
You have four graphs from which to choose.
Eliminate the first and second graphs; they are of expo decay functions.
Evaluate f(x) = (1/4)(4)^x at x = 0 to find the y-intercept:
f(0) = (1/4)(4)^0 = 1/4
Both the 3rd and the 4th graphs go through (0, 1/4). Good.
The 3rd graph shows the curve going through (3, 2). Let's determine whether or not this point lies on f(x) = (1/4)(4)^x:
f(3) = (1/4)(4)^2 = (1/4)(16) = 4. No.
The 4th graph shows the curve going through (1, 1). Does this point satisfy f(x) = (1/4)(4)^x? f(1) = (1/4)(4)^1 = 1. Yes.
The fourth graph is the correct choice.
