Find the domain of the following function.
$y=\frac{2x+3}{x-4}$

• A. $(-\infty ,\infty )$
• B. $\(\left\)(-\(\infty\),4\(\right\))\(\cup\[\left\)(4,\(\infty\]\right\))$
• C. $\(\left\)(-\(\infty\),4\(\right\]\rbrack\)$
• D. $\(\left\[\lbrack\)4,\(\infty\]\right\))$

Answer: (B)

Verified step by step guidance

1. Identify the function given: \(y=\frac{2x+3}{x-4}\). This is a rational function, which means the domain includes all real numbers except where the denominator is zero.
2. Set the denominator equal to zero to find values that are not allowed in the domain: \(x - 4 = 0\).
3. Solve the equation for \(x\): \(x = 4\). This value makes the denominator zero, which is undefined in mathematics.
4. Exclude \(x = 4\) from the set of all real numbers. The domain is all real numbers except \$4$.
5. Express the domain in interval notation as the union of two intervals: \(\left(-\infty,4\right) \cup \left(4,\infty\right)\).