Give a limit expression that describes the left end behavior of the function. \( f(x)=\frac{42 x^{7}+x^{2}}{16 x^{6}-2 x} \) \( \lim _{x \rightarrow-\infty} f(x)=\square \) (Simplify your answer.)

To analyze the left end behavior of the function \( f(x)=\frac{42 x^{7}+x^{2}}{16 x^{6}-2 x} \), we focus on the leading terms in both the numerator and the denominator as \( x \) approaches negative infinity. The leading term in the numerator is \( 42 x^7 \) and in the denominator, it is \( 16 x^6 \). Thus, the limit expression is: \[ \lim _{x \rightarrow-\infty} f(x) = \lim_{x \rightarrow -\infty} \frac{42 x^{7}}{16 x^{6}} = \lim_{x \rightarrow -\infty} \frac{42}{16} x = -\infty \]