Question

Determine whether the relations represent y as a function of x.

Answer 1

Both of those are functions.

Explanation:

`y=x^2` is a parabola that opens up.

Any upward or downward parabola is a function because they pass the vertical line test.

`x=\pm √(1-y){/tex]</p><p>Square both sides:</p><p>[tex]x^2=1-y`

Subtract 1 on both sides:

`x^2-1=-y`

Multiply both sides by -1:

`-x^2+1=y`

So this is a another parabola and it is faced down. So this is also a function.

`y=ax^2+bx+c` wit
`a \\eq 0` willl always be a parabola.

If
`a>0` then it is open up.

If
`a<0` then it is open down.

Upwards and downward parabolas will always be functions.

`x=ay^2+by+c` are also parabolas but these open to the left or right. These will not be functions because they will not pass the vertical line test.