Question

directions: for 1 - 6, use the graphs below to write limit statements for the end - behavior for each function.
1.
left:
right:
2.
left:
right:
3.
left:
right:
4.
left:
right:
5.
left:
right:
6.
left:
right:

Explanation:

Step1: Analyze left - hand end - behavior of \(f(x)\)

As \(x\to-\infty\), \(y = f(x)\to+\infty\), so \(\lim_{x\to-\infty}f(x)=+\infty\)

Step2: Analyze right - hand end - behavior of \(f(x)\)

As \(x\to+\infty\), \(y = f(x)\to+\infty\), so \(\lim_{x\to+\infty}f(x)=+\infty\)

Step3: Analyze left - hand end - behavior of \(g(x)\)

As \(x\to-\infty\), \(y = g(x)\to+\infty\), so \(\lim_{x\to-\infty}g(x)=+\infty\)

Step4: Analyze right - hand end - behavior of \(g(x)\)

As \(x\to+\infty\), \(y = g(x)\to-\infty\), so \(\lim_{x\to+\infty}g(x)=-\infty\)

Step5: Analyze left - hand end - behavior of \(h(x)\)

As \(x\to-\infty\), \(y = h(x)\to-\infty\), so \(\lim_{x\to-\infty}h(x)=-\infty\)

Step6: Analyze right - hand end - behavior of \(h(x)\)

As \(x\to+\infty\), \(y = h(x)\to-\infty\), so \(\lim_{x\to+\infty}h(x)=-\infty\)

Step7: Analyze left - hand end - behavior of \(k(x)\)

As \(x\to-\infty\), \(y = k(x)\to+\infty\), so \(\lim_{x\to-\infty}k(x)=+\infty\)

Step8: Analyze right - hand end - behavior of \(k(x)\)

As \(x\to+\infty\), \(y = k(x)\to+\infty\), so \(\lim_{x\to+\infty}k(x)=+\infty\)

Step9: Analyze left - hand end - behavior of \(p(x)\)

As \(x\to-\infty\), \(y = p(x)\to+\infty\), so \(\lim_{x\to-\infty}p(x)=+\infty\)

Step10: Analyze right - hand end - behavior of \(p(x)\)

As \(x\to+\infty\), \(y = p(x)\to-\infty\), so \(\lim_{x\to+\infty}p(x)=-\infty\)

Step11: Analyze left - hand end - behavior of \(m(x)\)

As \(x\to-\infty\), \(y = m(x)\to+\infty\), so \(\lim_{x\to-\infty}m(x)=+\infty\)

Step12: Analyze right - hand end - behavior of \(m(x)\)

As \(x\to+\infty\), \(y = m(x)\to-\infty\), so \(\lim_{x\to+\infty}m(x)=-\infty\)

Answer:

1. Left: \(\lim_{x\to-\infty}f(x)=+\infty\), Right: \(\lim_{x\to+\infty}f(x)=+\infty\)
2. Left: \(\lim_{x\to-\infty}g(x)=+\infty\), Right: \(\lim_{x\to+\infty}g(x)=-\infty\)
3. Left: \(\lim_{x\to-\infty}h(x)=-\infty\), Right: \(\lim_{x\to+\infty}h(x)=-\infty\)
4. Left: \(\lim_{x\to-\infty}k(x)=+\infty\), Right: \(\lim_{x\to+\infty}k(x)=+\infty\)
5. Left: \(\lim_{x\to-\infty}p(x)=+\infty\), Right: \(\lim_{x\to+\infty}p(x)=-\infty\)
6. Left: \(\lim_{x\to-\infty}m(x)=+\infty\), Right: \(\lim_{x\to+\infty}m(x)=-\infty\)