Question
upstudy study bank question image url

Describe the end behavior (long run behavior) of \( f(x)=-x^{8} \) As \( x \rightarrow-\infty, f(x) \rightarrow \) ? As \( x \rightarrow \infty, f(x) \rightarrow \) ? ?

Ask by Morgan Nguyen. in the United States
Mar 17,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

As \( x \) approaches negative infinity, \( f(x) \) approaches negative infinity. As \( x \) approaches positive infinity, \( f(x) \) also approaches negative infinity.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Beyond the Answer

As \( x \rightarrow -\infty, f(x) \rightarrow +\infty \). This is because the leading term \( -x^8 \) is negative, and since it's raised to an even power, the output will positive when \( x \) is a large negative number. As \( x \rightarrow \infty, f(x) \rightarrow -\infty \). Here, when \( x \) takes on large positive values, the term \( -x^8 \) becomes vastly negative due to the negative coefficient and the even exponent, leading \( f(x) \) to trend downwards.

Related Questions

Latest Pre Calculus Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy