Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

how to determine whether the equation defines y as a function of x. is it a function yes or no to the problem: x=y^2-6 and problem y=x^2+6

Sagot :

kate200468
[tex]A\ function\ is\ a\ special\ relationship\ between\ values:\\\\ to\ each\ value\ of\ x\ the\ rule\ assigns\ one\ and\ only\ one\ value\ of\ y.\\------------------------------\\y=x^2+6\ \ \ it\ is\ the\ function\\\\x=0\ \ \ \Rightarrow\ \ \ y=0^2+6=6\\x=-3\ \ \ \Rightarrow\ \ \ y=(-3)^2+6=9+6=15\\x=5\ \ \ \Rightarrow\ \ \ y=5^2+6=25+6=31\\------------------------------\\x=y^2-6\ \ \ it\ is\ not\ the\ function\\[/tex]

[tex]for\ example:\\x=3\ \ \ \ \Rightarrow\ \ \ \ 3=y^2-6\ \ \ \ \Rightarrow\ \ \ y^2=9\ \ \ \ \Rightarrow\ \ \ (y=3\ \ \ or\ \ \ y=-3)\\x=10\ \ \ \Rightarrow\ \ \ 10=y^2-6\ \ \ \Rightarrow\ \ \ y^2=16\ \ \ \Rightarrow\ \ \ (y=4\ \ \ or\ \ \ y=-4)\\x=75\ \ \ \Rightarrow\ \ \ 75=y^2-6\ \ \ \Rightarrow\ \ \ y^2=81\ \ \ \Rightarrow\ \ \ (y=9\ \ \ or\ \ \ y=-9)[/tex]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.