Question

s describe x = y and zº + yü - 25 completely. This includes finding the domain and range ofich equation, finding the important points such as intercepts, and descnbing what happensy as x increases4. How are these relationships different

Answer 1

For x = y²

`x=y^2`

This is an horizontal parabola

The domain is:

`\lbrack0,\infty)`

The range is:

`(-\infty,\infty)`

The y-intercept and the x-intercept are the same, it is the point (0,0).

As x increases y tends to infinity or minus infinity. Keep in mind y can be defined as:

`y=\pm\sqrt[]{x}`

For:

`x^2+y^2=25`

This is circle centered at origin with a radius of 5.

The domain is:

`\lbrack-5,5\rbrack`

The range is:

`\lbrack-5,5\rbrack`

The x-intercepts are:

`\begin{gathered} (-5,0) \\ and \\ (5,0) \end{gathered}`

The y-intercepts are:

`\begin{gathered} (0,-5) \\ and \\ (0,5) \end{gathered}`

As x increases, y decreases.