Question

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

Answer 1

Answer:

Both of those are functions.

Step-by-step 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 \sqrt{1-y}{/tex]

Square both sides:

[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 $a \neq 0$ 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.