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 growth value 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.

The growth value of the function is One-third ⇒ True (2nd)

The function shows exponential decay ⇒ True (3rd)

The function is a stretch of the function ⇒

True (4th)

Step-by-step explanation:

* Lets revise the form of the exponential function

- The general form of the exponential function is

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

- If b > 1, then f(x) is exponential growth function

- If 0 < b < 1, then f(x) is exponential decay function

* Lets solve the problem

- The exponential function

∴ The initial value is 3

∴ The growth factor is

∵ The growth factor is less than 1

∴ f(x) is exponential decay function

* Lets chose the true statements

# The initial value of the function is One-third ⇒ Not true

   because the initial value is 3

# The growth value of the function is One-third ⇒ True

   because the growth factor is

# The function shows exponential decay ⇒ True

   because the growth factor is less than 1

# The function is a stretch of the function

   ⇒ True

  because stretched vertically means multiply f(x) by constant greater

  than 1 and 3 is greater than 1

# The function is a shrink of the function ⇒ Not true

   because the growth factor is not 3

i think 5 miles per hour

step-by-step explanation: