$f(x)$ is a rational function given in both standard and factored forms.
Let $f(x)=\frac{3 x^{2}-14 x-24}{4 x^{2}-11 x+7}=\frac{(x-6)(3 x+4)}{(x-1)(4 x-7)}$
Find:
1) the domain in interval notation

Note: Use $-\infty 0$ for $-\infty, \infty$ for $\infty, \cup$ for union.
2) the $y$ intercept at the point
3) $x$ intercepts at the point(s)
4) Vertical asymptotes at $x=$
5) Horizontal asymptote at $y=$
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Step 1 ：Given the function $f(x)=\frac{3 x^{2}-14 x-24}{4 x^{2}-11 x+7}=\frac{(x-6)(3 x+4)}{(x-1)(4 x-7)}$, we need to find the domain, the $y$ intercept, $x$ intercepts, vertical asymptotes and horizontal asymptote.

Step 2 ：The domain of a rational function is all real numbers except for the values of $x$ that make the denominator equal to zero. So, we need to find the values of $x$ that make the denominator $4x^2 - 11x + 7 = 0$.

Step 3 ：Solving the equation $4x^2 - 11x + 7 = 0$, we get $x = 1$ and $x = \frac{7}{4}$. These are the values of $x$ that make the denominator of the function equal to zero, so they are not included in the domain of the function.

Step 4 ：Therefore, the domain of the function is $(-\infty, 1) \cup (1, \frac{7}{4}) \cup (\frac{7}{4}, \infty)$.

Step 5 ：Final Answer: The domain of the function in interval notation is \(\boxed{(-\infty, 1) \cup (1, \frac{7}{4}) \cup (\frac{7}{4}, \infty)}\).