is y!=x^2+2x+5 a function?

Question

its my home work plz help in my opinion its not cause we can not obtain any slopes for the curve

Answer 1

Because the factorial y! can have the same value for infinitely many y (all but one of which are negative), the inverse factorial is frequently said to be "not a function". However, the inverse factorial is nonetheless differentiable, as is the inverse factorial of x^2 + 2x + 5. It's just that it may have infinitely many slopes at a given x, because there can be infinitely many values for the inverse factorial of x^2 + 2x + 5 at a given x.

For visualization, you can plot (√(y-4) -1)! and understand that a reflection would be the function y that you seek.

A caveat: If this is a school homework, the teacher is probably going to expect you to say, "It's not a function". That's school for you.

Addendum: This is a parabola only if the exclaimation mark "!" denoting a factorial was a mistake, and it's just y = x^2 + 2x + 5.

Answer 2

very simble y!=x^2+2x+5 = (x^-1
+1)2x+5 = when a = 0 = (1/x+1)2x+5 When x = 0 = infintive when x = 1 y=9
when x = 1, 2 ......ect y= 11 and so on
when a = 1 (1*2+1)2x +5
when x = 1y = 11 when x = 2 y= 17
and so on

Answer 3

The derivative of this function will be obtained by using the product rule. The rule states that" if y=f(x) and f(x)=UV, then the derivative of y is given by, dy/dx=U.dV/dx+V.dU/dx". Since y=(x2+2)(2x-5). Let U=(x2+2) and V=(2x-5). dU/dx=d/dx(x2+2) dU/dx=2x. And dV/dx=d/dx(2x-5) dV/dx=2. From the rule, dy/dx=2(x2+2)+2x(2x-5). dy/dx=2x2+4+4x2-10 dy/dx=6x2-6 dy/dx=6(x2-1). This is the derivative of the function. Thanx!!!

Answer 4

Yes. It will be a parabola, which looks like a smile. Try using a graphing calculator or substituting values in for x and making a table.