Consider the function $f(x)=-3x^2+12x-3$
a. Determine, without graphing, whether the function has a minimum value or a maximum value.
b. Find the minimum or maximum value and determine where it occurs.
c. Identify the function's domain and its range.
a. The function has a value.

Step 1 ：The function given is $f(x)=-3x^2+12x-3$.

Step 2 ：Since the coefficient of $x^2$ is negative, the function opens downwards. Therefore, the function has a maximum value.

Step 3 ：The maximum value of a quadratic function $f(x)=a{x}^2+bx+c$ occurs at $x=-\frac{b}{2a}$.

Step 4 ：Substituting $a=-3$ and $b=12$ into the formula, we get $x=-\frac{12}{2(-3)}=2$.

Step 5 ：The maximum value of the function is $f(2)=-3(2{)}^2+12(2)-3=9$.

Step 6 ：The domain of the function is all real numbers, because any real number can be substituted for $x$ in the function.

Step 7 ：The range of the function is $y\le 9$, because the maximum value of the function is 9 and the function opens downwards.

Step 8 ：$\boxed{{\displaystyle \text{Final Answer:}}}$ The function $f(x)=-3x^2+12x-3$ has a maximum value of 9 at $x=2$. The domain of the function is all real numbers and the range is $y\le 9$.