The blueprint design shows that a section of a ramp can be modeled using a rational function of the form: \[ f(x)=\frac{2}{5 x+8} \] Find the domain of the function. Express the exact answer using interval notation. To enter $\infty$, type infinity. To enter $\cup$, type $U$.

Step 1 ：The blueprint design shows that a section of a ramp can be modeled using a rational function of the form: \(f(x)=\frac{2}{5 x+8}\). We are asked to find the domain of this function.

Step 2 ：The domain of a function is the set of all possible input values (x-values) that will output real numbers. For a rational function, the domain is all real numbers except for any values that would make the denominator equal to zero.

Step 3 ：To find the value of x that makes the function undefined, we need to solve the equation \(5x + 8 = 0\).

Step 4 ：Solving the equation gives us \(x = -\frac{8}{5}\). This is the value that makes the function undefined.

Step 5 ：Therefore, the domain of the function is all real numbers except for \(x = -\frac{8}{5}\).

Step 6 ：We can express this in interval notation as \((- \infty, -\frac{8}{5}) \cup (-\frac{8}{5}, \infty)\).

Step 7 ：\(\boxed{The domain of the function is (- \infty, -\frac{8}{5}) \cup (-\frac{8}{5}, \infty)}\)