Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A 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 stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.