c. Suppose $f(x)=\frac{x^{5}+4 x^{3}+3 x+1}{x^{3}+17}$. As $x \rightarrow \pm \infty, f(x)$ behaves like: \[ y= \] Preview

Step 1 ：Suppose we have the function \(f(x)=\frac{x^{5}+4 x^{3}+3 x+1}{x^{3}+17}\).

Step 2 ：As \(x\) approaches positive or negative infinity, the highest degree term in the numerator and denominator will dominate the behavior of the function.

Step 3 ：In this case, the highest degree term in the numerator is \(x^5\) and in the denominator is \(x^3\).

Step 4 ：Therefore, as \(x \rightarrow \pm \infty\), \(f(x)\) will behave like \(\frac{x^5}{x^3}\), which simplifies to \(x^2\).

Step 5 ：\(\boxed{As \(x \rightarrow \pm \infty\), \(f(x)\) behaves like \(y = x^2\)}\).