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

Answer 1

Interpret f(x) = (1/4)·4^x. Rewrite f(x) = 4^{x}/4 = 4^{x-1}.

So f(1) = 4^{0} = 1 and f(2) = 4^{1} = 4. As x → −∞ the graph approaches y = 0 (positive y for negative x, i.e. in quadrant II), and the function is increasing (curves up to the right).

Therefore the correct graph is the one described last: "approaches y = 0 in quadrant 2 and goes through points (1, 1) and (2, 4)."