Question

Which function is graphed below?

On a coordinate plane, an exponential decay function is shown. The curve starts in quadrant 2 and decreases into quadrant 1. It crosses the y-axis at (0, 3) and approaches y = 0 in quadrant 1.
y = one-third (3) Superscript x
y = 3 (one-third) Superscript x
y = (one-half) Superscript x Baseline + 2
y = (2) Superscript x Baseline minus 1

Answer 1

The correct exponential decay function that matches the given graph is y = 3 (⅓)x, where the graph starts in quadrant 2, crosses the y-axis at (0, 3), and approaches y = 0 as x increases.

Step-by-step explanation:

The graph described in the question indicates that it represents an exponential decay function. It starts in quadrant 2, crosses the y-axis at (0, 3), and approaches y = 0, which suggests that the function's form will be y = abx where 0 < b < 1, since b represents the decay rate. Given that it crosses the y-axis at (0, 3), we can determine that a (the initial value) is 3. Since the graph heads towards y = 0 as x increases, the base b of the exponential must be less than 1.

The correct function represented by the graph is y = 3 (⅓)x. Here, '⅓' refers to the fraction one-third. When x = 0, this function yields y = 3 * (⅓)0 = 3 * 1 = 3, matching the intersection point described. As x increases, the function approaches zero, indicating exponential decay consistent with the function's definition.