Chapter 4.2, Problem 1QR

To determine

To calculate: To sketch the curve defined by the equation $x-y^2=0$ and find two functions $y_1\text{ and }{y}_2$ whose graphs will combine to give the curve.

Answer to Problem 1QR

The graph of the curve is shown above.

The two curves are $y=\sqrt{x}\text{ and }y=-\sqrt{x}$.

Explanation of Solution

Given Information: The equation of the curve is $x-y^2=0$

Calculation:

The graph of the curve represents a parabola having vertex at $\left(0,0\right)$ and has a right opening. The graph of the curve $x-y^2=0$ is,

  

To find the two functions which combine to form the above curve, simplify the equation of curve,

  $\begin{array}{c}x-y^2=0\\ y^2=x\\ y=\pm \sqrt{x}\end{array}$

Hence, the two curves are $y=\sqrt{x}\text{ and }y=-\sqrt{x}$