In this problem, we must find the end behaviour of y as x tends to infinity in the equation:
[tex]y=-2x^3.[/tex]• Taking the limit for x → -∞, we have:
[tex]\lim_{x\to-\infty}(-2x^3)=-2\lim_{x\to-\infty}(x^3)=-2\cdot(\lim_{x\to-\infty}x)^3=-2\cdot(-\infty)^3=-2\cdot(-\infty)=+\infty.[/tex]• Taking the limit for x → +∞, we have:
[tex]\lim_{x\to+\infty}(-2x^3)=-2\lim_{x\to+\infty}(x^3)=-2\cdot(\lim_{x\to+\infty}x)^3=-2\cdot(+\infty)^3=-2\cdot(+\infty)=-\infty.[/tex]Answer• When x → -∞, the function y tends to +∞
• When x → +∞, the function y tends to -∞
