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

The true statements are; b. The growth value of the function is One-third. c. The function shows exponential decay. d. The function is a stretch of the function.  $f(x) = \frac{1}{3} ^x$

What is an exponential function?

The general form of the exponential function;

$f(x) = a b ^x$

where "a" is the initial amount and "b" is the growth factor

The given exponential function

$f(x) = 3(\frac{1}{3} )^x$

here,

The initial value is 3

The growth factor is 1/3

The growth factor is less than 1

Therefore,  f(x) is exponential decay function.

The true statements are;

b. The growth value of the function is One-third.

c. The function shows exponential decay.

d. The function is a stretch of the function.  $f(x) = \frac{1}{3} ^x$

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