Question

Determine the y-intercept and the end behavior of the following function

Answer 1

\[y = 5x ^{12} + 43x^8 - 14x^5 + 12x^2 + 8x\]

y-intercept: 0

\[x \rightarrow -\infty , y \rightarrow +\infty\]
\[x \rightarrow +\infty, y \rightarrow +\infty\]

This is due to 5x^12 having a positive coefficient and an even degree of 12.