List the domain and the $$ x $$ - and $$ y $$-intercepts of the following function. Graph the function. Be sure to label all the asymptotes. $$ f(x)=\frac{x^{2}+2 x-8}{7 x^{2}+4} $$ What is the domain of the function? (Type your answer in interval notation.)

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1. Write the function:  
   $$
   f(x)=\frac{x^2+2x-8}{7x^2+4}
   $$

2. Determine the domain by finding when the denominator is nonzero. The denominator is:  
   $$
   7x^2+4
   $$

3. Set the denominator equal to zero and solve:  
   $$
   7x^2 + 4 = 0
   $$
   $$
   7x^2 = -4
   $$
   $$
   x^2 = -\frac{4}{7}
   $$
   Since $$ x^2 $$ cannot be negative for real values of $$ x $$, there are no real solutions.

4. Since the denominator is never zero, the function is defined for all real numbers.

5. Therefore, the domain of $$ f(x) $$ in interval notation is:  
   $$
   (-\infty, \infty)
   $$
The domain of the function $$ f(x) = \frac{x^2 + 2x - 8}{7x^2 + 4} $$ is all real numbers, which can be written in interval notation as $$ (-\infty, \infty) $$.

List the domain and the - and -intercepts of the following function. Graph the function. Be sure to label all the asymptotes.

What is the domain of the function?
(Type your answer in interval notation.)

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List the domain and the - and -intercepts of the following function. Graph the function. Be sure to label all the asymptotes. What is the domain of the function? (Type your answer in interval notation.)