Question

Which is the graph of f(x) = one-fourth(4)x?

On a coordinate plane, an exponential function approaches y = 0 in quadrant 1. It curves up to the left and goes through points (2, 1) and (0, 4).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 1. It curves up to the left and goes through points (1, 1) and (0, 4).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and goes through points (3, 2) and (4, 4).

Answer 1

I need to check how you meant the formula — "one-fourth(4)x" is ambiguous. Do you mean any of these common interpretations?
- f(x) = (1/4)·4^x
- f(x) = 4·(1/4)^x (equivalently 4^{1−x})
- f(x) = 4·(1/2)^x (equivalently 4·2^{−x})
- f(x) = (1/4)·2^x

Which one did you mean?

Quick guide so you can match to the three pictured graphs:
- f(x) = (1/4)·4^x = 4^{x−1} passes through (1,1) and (2,4). (None of your three descriptions lists that pair.)
- f(x) = 4·(1/4)^x passes through (0,4) and (1,1) and has horizontal asymptote y=0 on the right — this is the second graph you described.
- f(x) = 4·(1/2)^x passes through (0,4) and (2,1) and has y→0 as x→+∞ — this matches the first graph you described.
- f(x) = (1/4)·2^x passes through (3,2) and (4,4) (since it doubles when x increases by 1 there) — this matches the third graph.

Tell me which algebraic form you intended and I’ll pick the correct graph.