Question

Consider the exponential function f(x) = 3(one-third) Superscript x and its graph.

On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 3) and goes through (1, 1).
Which statements are true for this function and graph? Select three options.

The initial value of the function is One-third.
The base of the function is One-third.
The function shows exponential decay.
The function is a stretch of the function f(x) = (one-third) Superscript x.
The function is a shrink of the function f(x) = 3x

Answer 1

Correct choices:
- The base of the function is One-third. (True: f(x) = 3*(1/3)^x, so base = 1/3.)
- The function shows exponential decay. (True: base 1/3 is between 0 and 1, so the function decreases as x increases.)
- The function is a stretch of the function f(x) = (one-third)^x. (True: f(x) = 3·(1/3)^x is a vertical stretch of (1/3)^x by factor 3.)

The other two statements are false: the initial value (y-intercept) is f(0) = 3, not 1/3, and the function is not a shrink of f(x) = 3x (and it is not a shrink of 3^x either).