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

Answer:

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 $f(x)=(\frac{1}{3})^{x}$ ⇒

True (4th)

Step-by-step 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 $f(x)=3(\frac{1}{3})^{x}$

∴ The initial value is 3

∴ The growth factor is $\frac{1}{3}$

∵ 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 $\frac{1}{3}$

# The function shows exponential decay ⇒ True

   because the growth factor is less than 1

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

   ⇒ 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

Answer 2

Answer:

the second, third, and fourth answer

Step-by-step explanation:

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