Respuesta :
Answer:
The initial value is 3.
The range is y greater than 0.
The simplified base is 8.
Step-by-step explanation:
The given function is [tex]f(x) = 3(16)^{\frac{3}{4}x }[/tex] ......... (1)
Therefore, the initial value of the function at x = 0 is [tex]f(0) = 3(16)^{0} = 3[/tex]
Now, the domain can be any real value, since for all real value of x, y exists.
But, for no value of x the function has value < 0.
Therefore, y greater than 0 is the range of the function f(x).
Now, simplifying the equation (1) we will have
[tex]f(x) = 3(16)^{\frac{3}{4}x } = 3(16^{\frac{3}{4} } )^{x} = 3(8)^{x}[/tex]
Therefore, the simplified base is 8. (Answer)
Answer:
The true statements include
- The initial value is 3.
- The range is y >0.
- The simplified base is 8.
Step-by-step explanation:
f(x) = 3 (16^0.75x) = 3 (16⁰•⁷⁵ˣ)
We will check each of the options for how true they are.
- The initial value is 3.
The initial value of a function is when x=0
and when x=0
f(x) = 3 (16⁰•⁷⁵ˣ)
At x = 0
f(x) = 3 (16⁰) = 3 × 1 = 3.
This statement is true as the the initial value of the function is indeed 3.
- The domain is x>0
The domain of a function refers to the region of values of x where the funcfion exists.
f(x) = 3 (16⁰•⁷⁵ˣ)
It is evident that f(x) will exist any where for any real number value of x. Especially for regions where x ≤ 0, contrary to this statement. Hence, this statement is false.
- The range is y >0.
The range of a function is the set of numbers or region or interval of values that the function can take on.
f(x) = 3 (16⁰•⁷⁵ˣ)
It is evident that this function will always be positive. Hence, the range is truly y>0.
This statement is true.
The last two statements will be solved similarly
f(x) = 3 (16⁰•⁷⁵ˣ)
To simplify This,
f(x) = 3 (2⁴)⁰•⁷⁵ˣ = 3 (2³ˣ) = 3 (8ˣ)
The simplified base is evidently 8.
- The simplified base is 12.
This statement is not evidently true.
- The simplified base is 8.
This statement is true.
Hope this Helps!!!
