Which is the graph of f(x) = 1/4 (4)x?
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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.

the answer is 5/3x+7/5y+7

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step-by-step explanation: