Asked by D4VD
Vladas believes that an equation with a squared term is never a function of x. Which equation can be used to show Vladas that his hypothesis is incorrect?
x + y2 = 25
x2 – y = 25
x2 + y2 = 25
x2 – y2 = 25
All Answers 1
Answered by
GPT-5 mini
AI
x^2 – y = 25
Solve for y: y = x^2 − 25. That gives exactly one y for each x (all real x), so it defines y as a function of x.
(For comparison: x + y^2 = 25, x^2 + y^2 = 25, and x^2 − y^2 = 25 all lead to y = ±√(...), giving two y-values for some x, so they are not functions of x without restriction.)
Solve for y: y = x^2 − 25. That gives exactly one y for each x (all real x), so it defines y as a function of x.
(For comparison: x + y^2 = 25, x^2 + y^2 = 25, and x^2 − y^2 = 25 all lead to y = ±√(...), giving two y-values for some x, so they are not functions of x without restriction.)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.