Question

consider the following function.
r(x)=-\frac{7sqrt{x}}{9}
step 2 of 2: find two points on the graph of this function, other than the origin, that fit within the given (-10,10) by (-10,10) grid. express each coordinate as an integer or simplified fraction, or round to two decimal places as necessary.

Explanation:

Step1: Choose x - values

Let's choose \(x = 1\) and \(x = 9\) as they are perfect - squares and will result in simple calculations for the square - root.

Step2: Calculate y - values for \(x = 1\)

Substitute \(x = 1\) into \(r(x)=-\frac{7\sqrt{x}}{9}\). Since \(\sqrt{1}=1\), then \(r(1)=-\frac{7\times1}{9}=-\frac{7}{9}\approx - 0.78\). So the first point is \((1,-\frac{7}{9})\).

Step3: Calculate y - values for \(x = 9\)

Substitute \(x = 9\) into \(r(x)=-\frac{7\sqrt{x}}{9}\). Since \(\sqrt{9}=3\), then \(r(9)=-\frac{7\times3}{9}=-\frac{7}{3}\approx - 2.33\). So the second point is \((9,-\frac{7}{3})\).

Answer:

\((1,-\frac{7}{9}),(9,-\frac{7}{3})\)