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Which of these statements is true for f(x)=5*(6)^x?
A. The domain of f(x) is x>0.
B. The y-intercept is (0,1).
C. It is always decreasing.
D. The y-intercept is (0,5).

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The answer is D cause y represents 5 in this case
varshamittal029

D. The y-intercept is (0,5) of the function 5*(6)ˣ

Which one is the correct option ?

Given function is f(x) = 5*(6)ˣ

Now we have to choose correct statement from the given options.

Option A: The domain of f(x) is x>0.

Exponential functions are of the form f(x) = a*bˣ

Also the given function is in exponential function.

For any exponential function, domain is the set of real numbers not only x>0,

So this option is false.

Option B : The y-intercept is (0,1).

y-intercept means the value of x is 0.

f(0) = 5*6⁰

⇒ f(0) = 5 ≠ 1

So this option is false.

Option C :  It is always decreasing.

Exponential functions are of the form f(x) = a*bˣ

The function will be increasing, if b>1

Given function is f(x) = 5*(6)ˣ

As 6>1, we can say that the function is increasing function.

So this option is false.

Option D : The y-intercept is (0,5).

y-intercept means the value of x is 0.

f(0) = 5*6⁰

⇒ f(0) = 5

So, the y-intercept is (0, 5).

So this option is true.

Learn more about functions here :

https://brainly.com/question/27447037

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