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

True statements (choose three):

- The base of the function is One-third.
Reason: f(x) = 3*(1/3)^x so the base b = 1/3.

- The function shows exponential decay.
Reason: 0 < b = 1/3 < 1, so the function decreases as x increases.

- The function is a stretch of the function f(x) = (one-third)^x.
Reason: f(x) = 3*(1/3)^x is 3 times (1/3)^x, a vertical stretch by factor 3.

False statements:

- The initial value of the function is One-third. (False: f(0)=3.)
- The function is a shrink of the function f(x)=3x. (False: that compares different function types; ours is not a shrink of the linear function 3x.)