Question

Which of the following explains why f(x) = log4x does not have a y-intercept? Check all that apply.

1. There is no power of 4 that is equal to 0.


2. There is no power of 4 that is equal to 1.


3. Its inverse does not have any x-intercepts.


4. Its inverse does not have any y-intercepts.
NEED ANSWER ASAP!!!!!

Answer 1

There is no power of 4 that is equal to 0.

Its inverse does not have any x-intercepts.

Explanation:

Answer 2

The correct options are 1 and 3.

Explanation:

The given function is

`f(x)=log_4x`

It can be written as

`y=log_4x`

`4^y=x` .... (1)
`[\because y=log_ax\Rightarrow a^y=x]`

At y-intercept, the value of x is 0.

`4^y=0`

For any value of y, this statement is not true. It means there is no power of 4 that is equal to 0.

Option 1 is correct.

Interchange x and y in equation 1 to find the inverse of the function.

`4^x=y`

This function does not have any x-intercepts. because for any value of x, the value of y can not be 0.

Since the inverse function have not x-intercept, therefore the function have no y-intercept.

Option 3 is correct.