Question

p(x)=2x⎯⎯√5/3 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.

Answer 1

The function p(x) = \frac{2x}{\sqrt{5/3}} yields two points within the [-10,10] grid at approximately (3, 4.71) and (-4, -6.29) when using integer values for x.

Step-by-step explanation:

The function given is p(x) = \frac{2x}{\sqrt{5/3}}. To find two points on this graph, let's choose integer values for x and calculate their corresponding y values, ensuring the points fit within the given [−10,10] by [−10,10] grid.

Let's calculate p(3) and p(-4):

• p(3) = \frac{2(3)}{\sqrt{5/3}} = \frac{6\sqrt{3}}{\sqrt{5}} \approx 4.71
• p(-4) = \frac{2(-4)}{\sqrt{5/3}} = \frac{-8\sqrt{3}}{\sqrt{5}} \approx -6.29

Thus, the two points on the graph of this function within the [-10,10] by [-10,10] grid are approximately (3, 4.71) and (-4, -6.29).

To find two points on the graph of the function p(x) = 2x - √5/3 that fit within the given grid, we need to substitute values of x and solve for y.

Let's choose x = 1. Substituting this value into the equation, we get:

p(1) = 2(1) - √5/3 = 2 - √5/3

This gives us the point (1, 2 - √5/3).

Now, let's choose x = 2. Substituting this value into the equation, we get:

p(2) = 2(2) - √5/3 = 4 - √5/3

This gives us the point (2, 4 - √5/3).