Question

Consider the exponential function f(x) = 3(^x). Which statements are true for this function and its graph? Select three options.

(a) The initial value of the function is 2/2.
(b) The base of the function is e.
(c) The function shows exponential decay.
(d) The function is a stretch of the function f(x) = 3^x.
(e) The function is a shrink of the function f(x) = 3.

Answer 1

The statements that are true for the exponential function f(x) = 3^x and its graph are: (c) The function shows exponential decay, (d) The function is a stretch of the function f(x) = 3^x.

Step-by-step explanation:

Statements (b), (c), and (d) are true for the exponential function f(x) = 3^x.

1. (b) The base of the function is e is false as the base of the function is 3.
2. (c) The function shows exponential decay is true. As x increases, the value of f(x) decreases exponentially.
3. (d) The function is a stretch of the function f(x) = 3^x is true. The graph of f(x) = 3^x is horizontally stretched by a factor of 2.