Given the following exponential function,
\[
f(x)=\left(4^{1-x}\right)-2
\]

Fill in the blanks below: For each blank your answer should be submitted with no spaces between any characters. Coordinate points must be written with brackets and equations must be written correctly: $y=$. or $\mathrm{x}=$ For the domain, signs must be used to specify -inf or +inf and appropriate brackets must be specified.

The coordinates of the $y$-intercept is:
A
The coordinates of the $\mathrm{x}$-intercept is:
A
The mathematical domain is:
A
The equation of the horizontal asymptote is:
$A$
The range is:
A

Step 1 ：Given the exponential function \(f(x)=4^{1-x}-2\)

Step 2 ：Substitute \(x = 0\) into the function to find the y-intercept, which gives \(y = 2\). So, the coordinates of the y-intercept are \(\boxed{(0, 2)}\)

Step 3 ：Solve the equation \(f(x) = 0\) to find the x-intercept. However, the x-intercept also has a complex part, which means the function does not cross the x-axis at a real number. Therefore, there is no real x-intercept for this function. So, the coordinates of the x-intercept is \(\boxed{\text{None}}\)

Step 4 ：The mathematical domain of the function is all real numbers, which is \(\boxed{(-\infty, +\infty)}\)

Step 5 ：The equation of the horizontal asymptote is \(y = -2\), which is \(\boxed{y = -2}\)

Step 6 ：The range of the function is \((-2, +\infty)\), which is \(\boxed{(-2, +\infty)}\)