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 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.

Answer 1

the second, third, and fourth answer

Explanation:

i took the test

Answer 2

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
`f(x)=((1)/(3))^(x)` ⇒

True (4th)

Explanation:

* Lets revise the form of the exponential function

- The general form of the exponential function is
`f(x)=a(b)^(x)`

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
`f(x)=3((1)/(3))^(x)`

∴ The initial value is 3

∴ The growth factor is
`(1)/(3)`

∵ 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
`(1)/(3)`

# The function shows exponential decay ⇒ True

because the growth factor is less than 1

# The function is a stretch of the function
`f(x)=((1)/(3))^(x)`

⇒ 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
`f(x)=(3)^(x)` ⇒ Not true

because the growth factor is not 3