give the domain and range?

Question

of the equation and indicate whether or not it is a function

x=ysquared + 9


can you please show work . thank you. and i'm pretty sure you have to set y = to the rest or osemthing like that

Answer 1

Let's say this way:x=y^2+9

as we know y^2>=0, therefore: x>=9

On d other hand for finding the range,you should make x alone(!) & solve d equation of y: y^2-x+9=0 .as u see this equation always occures for all d amounts of y,considering the given domain.so: y belongs to the Rational numbers.

Now let's check if It is afunction or not.
d best way that I can clearly explain it to u through writing & limited charackters on d key board,is this.

*Consider F(x) as a function,therefore we have
(x1,y1) , (x2,y2) belongs to F
if x1=x2 therefore y1=y2

It simply says If the first amounts(x) are equal then the second ones(y) should be equal too.

Now we do vice verca:
x1=x2
therefore: y1^ 2+9=y2^2+9
Now subtract 9s from both sides: y1^2=y2^2
y1^2-y2^2=0
(y1+y2)(y1-y2)=0
so we will have: y1=y2
or
y1=-y2
as we didn't reach the *consideration above,It cannot be a function.
(u can also draw it & check If it is a function or not,I really don't know how to explain it through this!)

*Extra Practice: Dicate wether these are function or not:
1)x=sin y
2)lxl =lyl+1

Answer 2

x = y^2 + 9

First off, this isn't a function, as this is a sideways parabola which opens to the right. This implies that it fails the vertical line test.

To determine the domain and range of this function, all you have to do is swap the x and y terms. Upon doing so, this new function's domain will be this function's range, and that function's range will be this function's domain.

y = x^2 + 9

This is a parabola, shifted 9 units upward.

The domain is all real numbers.
The range is the vertex of this parabola, upward; that is, the range is the set of all x such that x is greater than or equal to 9.

Therefore, for

x = y^2 + 9

The domain is the set of all x such that x is greater than or equal to 9.
The range is all real numbers.

See how the domain and range swapped, after the x and y values swapped?