Given the following logarithm function,
\[
f(x)=2 \log _{4}(2-x)-2
\]

Fill in the blanks below. For each blank your answer should be submitted with no spaces between any characters. Coordinate points require brackets and equations of lines should be written as $x=\ldots$ or $y=\ldots$ You must specify the sign of infinity (either +inf or -inf) when writing an interval.

The $y$-intercept is:
A
The $\mathrm{x}$-intercept is:
A
The mathematical domain is:

The equation of the Vertical Asymptote is:
A

Step 1 ：To find the y-intercept, we set x = 0 in the function: \(f(0)=2 \log _{4}(2-0)-2 = 2 \log _{4}(2)-2 = 2*0.5 - 2 = 1 - 2 = -1\). So, the y-intercept is \(\boxed{(0, -1)}\).

Step 2 ：To find the x-intercept, we set f(x) = 0 in the function: \(0=2 \log _{4}(2-x)-2\). Solving this equation gives us: \(2 = 2 \log _{4}(2-x)\). Dividing both sides by 2 gives us: \(1 = \log _{4}(2-x)\). Using the property of logarithms, we can rewrite this as: \(4^1 = 2 - x\). Solving for x gives us: \(x = 2 - 4 = -2\). So, the x-intercept is \(\boxed{(-2, 0)}\).

Step 3 ：The domain of a logarithmic function is the set of all real numbers for which the function is defined. In this case, the function is defined for all x such that 2 - x > 0. Solving this inequality gives us x < 2. So, the domain is \(\boxed{(-\infty, 2)}\).

Step 4 ：The vertical asymptote of a logarithmic function is the vertical line x = a, where a is the value that makes the argument of the logarithm equal to zero. In this case, the argument of the logarithm is 2 - x, so the vertical asymptote is the line \(\boxed{x = 2}\).