Answer:
# The growth value of the function is 1/3 ⇒ 2nd
# f(x) shows exponential decay ⇒ 3rd
# The function is a stretched of the function [tex]f(x)=(\frac{1}{3}) ^{x}[/tex] ⇒ 4th
Step-by-step explanation:
* Lets explain the exponential function
- The form of the exponential function is f(x) = a b^x, where a ≠ 0,
b > 0 , b ≠ 1, and x is any real number
- a is the initial value of f(x) ⇒ (when x = 0)
- b is the growth factor
- The exponent is x
- If the growth factor (b) is in between 1 and 0 then it is exponential
decay
* Lets solve the problem
∵ [tex]f(x)=3(\frac{1}{3})^{x}[/tex]
- Lets find the initial value
∵ At the initial position x = 0
∴ [tex]f(0)=3(\frac{1}{3})^{0}=3(1)=3[/tex]
* The initial of f(x) is 3
∵ b = 1/3
∵ b is the growth factor of the function
* The growth value of the function is 1/3
∵ b = 1/3
∵ 0 < b < 1
∴ The function is exponential decay
* f(x) shows exponential decay
- A vertical stretching is the stretching of the graph away from the x-axis
- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched
∵ [tex]f(x)=(\frac{1}{3})^{x}[/tex]
∵ Its parent function is [tex]f(x)=3(\frac{1}{3})^{x}[/tex]
∴ k = 3
∵ k > 1
∴ the function is stretched vertically
* The function is a stretched of the function [tex]f(x)=(\frac{1}{3})^{x}[/tex]
∴ The true statements are:
# The growth value of the function is 1/3
# f(x) shows exponential decay
# The function is a stretched of the function [tex]f(x)=(\frac{1}{3})^{x}[/tex]
