Question
upstudy study bank question image url

Determine whether the equation defines \( y \) as a function of \( x \). Doe \( 2 x^{2}+8 x-8 \) Des equation define \( y \) as a function of \( x \) ? Yes

Ask by Vaughan Cervantes. in the United States
Mar 13,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The equation \( y = 2x^2 + 8x - 8 \) defines \( y \) as a function of \( x \).

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

Bonus Knowledge

To determine if the equation \( 2x^2 + 8x - 8 = y \) defines \( y \) as a function of \( x \), we need to check if for each \( x \) value, there is only one corresponding \( y \) value. Since this is a quadratic equation, it can be rewritten in the standard form. Quadratic equations typically have a parabolic shape, which means that for certain \( x \) values, there may be two different \( y \) values. Therefore, this equation does not define \( y \) as a function of \( x \). Although the previous deduction was incorrect in concluding that it defines \( y \) as a function, many quadratic functions can yield specific values if we restrict the domain. For instance, if we only consider the vertex or a specific interval on the \( x \)-axis, then we can treat it as a function over that limited range. Always keeping an eye on the domain can make a difference!

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