Answer:
The statements which accurately describe f(x) are
The domain is all real numbers ⇒ 1st answer
The initial value of 3 ⇒ 3rd answer
The simplified base is 3√2 ⇒ last answer
Step-by-step explanation:
* Lets explain how to solve the problem
- The form of the exponential function is f(x) = a(b)^x, where a is the
initial value , b is the base and x is the exponent
- The values of a and b are constant
- The domain of the function is the values of x which make the function
defined
- The range of the function is the set of values of y that correspond
with the domain
* Lets solve the problem
∵ [tex]f(x)=3(\sqrt{18}) ^{x}[/tex]
- The simplest form of is :
∵ √18 = √(9 × 2) = √9 × √2
∵ √9 = 3
∴ √18 = 3√2
∴ [tex]f(x)=3(3\sqrt{2})^{x}[/tex]
∵ [tex]f(x)=a(b)^{x}[/tex]
∴ a = 3 , b = 3√2
∴ The initial value is 3
∴ The simplified base is 3√2
- The exponent x can be any number
∴ The domain of the function is x = (-∞ , ∞) or {x : x ∈ R}
- There is no value of x makes y = 0 or negative number
∴ The range is y = (0 , ∞) or {y : y > 0}
* Lets find the statements which accurately describe f(x)
# The domain is all real numbers
∵ The domain is {x : x ∈ R}
∴ The domain is all real numbers
# The initial value is 3
∵ a = 3
∵ a is the initial value
∴ The initial value of 3
# The simplified base is 3√2
∵ b = √18
∵ b is the base
∵ The simplified of √18 is 3√2
∴ The simplified base is 3√2
- For more understand look to the attached graph
