For the graph of $R(x)=\frac{x(x-15)^{2}}{(x-15)}$, find the following. a. Find the domain of $R$. b. Find the $x$-intercepts of $R$.

Step 1 ：The first question asks for the domain of the function $R(x)=\frac{x(x-15)^{2}}{(x-15)}$. The domain of a function is the set of all possible input values (often the 'x' variable), which produce a valid output from a particular function. In this case, we need to find all the values of $x$ for which $R(x)$ is defined.

Step 2 ：The function $R(x)$ is defined for all real numbers except for the values of $x$ that make the denominator zero, because division by zero is undefined in mathematics. Therefore, we need to find the values of $x$ that make $(x-15)$ equal to zero.

Step 3 ：Let's solve the equation $(x-15) = 0$ to find the values of $x$ that are not in the domain of $R(x)$.

Step 4 ：The value of $x$ that makes the denominator of $R(x)$ equal to zero is $x=15$. Therefore, the domain of $R(x)$ is all real numbers except $x=15$.

Step 5 ：Final Answer: The domain of $R$ is \(\boxed{x \in \mathbb{R}, x \neq 15}\).