Exponential Functions — Test

Question 23 • Mathematics I

Which is the graph of f of x is equal to 4 times 1 half to the x th power ?

Answer

Image with description On a coordinate plane, an exponential decay function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 2) and goes through (1, 1).

Image with description On a coordinate plane, an exponential decay function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 4) and goes through (1, 1).

Image with description On a coordinate plane, an exponential decay function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 2) and goes through (1, 0.5).

Image with description On a coordinate plane, an exponential decay function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 4) and goes through (2, 1).

Explanation

At x = 0, f(0) = 4(1/2)^0 = 4, so the graph crosses the y-axis at (0, 4). At x = 2, f(2) = 4(1/2)^2 = 1, so it also passes through (2, 1). This matches the graph described in choice D.

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