Consider the following function.

h(x)=−5/6x^3
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 four decimal places as necessary.
A: (_,_)
B: (_,_)

To find two points on the graph of the function h(x) = -5/6x^3 within the given grid of -10,10 times-10,10, we can choose x-values within this range and calculate the corresponding y-values using the function.

1. Let's start by selecting x = -2: Substitute x = -2 into the function: \( h(-2) = -5/6(-2)^3 = -5/6(-8) = 40/6 = 20/3.Therefore, the point A on the graph is (-2, 20/3).

2. Next, let's choose x = 3: Substitute x = 3 into the function: \( h(3) = -5/6(3)^3 = -5/6(27) = -135/6= -45/2.Thus, the point B on the graph is (3, -45/2).

Therefore, the two points on the graph of the function within the grid of -10,10 times -10,10are: A: (-2, 20/3) B: (3, -45/2) These points can be plotted on a graph to visualize the function's behavior within the specified range.

Hope this helps! :D

msm555 msm555 · Answer 2 · 2024-02-22T02:49:14+01:00

Answer:

A: [tex](2, -6.6667)[/tex]

B: [tex](-2, 6.6667)[/tex]

Step-by-step explanation:

To find two points on the graph of:

[tex] h(x) = -\dfrac{5}{6}x^3 [/tex]

within the given grid [tex][-10,10] \times [-10,10][/tex], we can simply substitute the [tex]x[/tex] values and compute the corresponding [tex]y[/tex] values.

We can select variables between -10 to 10.

So,

Let's choose [tex]x = 2[/tex] and [tex]x = -2[/tex] .

For [tex]x = 2[/tex]:

[tex] h(2) = -\dfrac{5}{6}(2)^3 \\\\ = -\dfrac{5}{6}(8) \\\\ = -\dfrac{40}{6} \\\\ = -\dfrac{20}{3} \\\\ = - 6.6667 [/tex]

For [tex]x = -2[/tex]:

[tex] h(-2) = -\dfrac{5}{6}(-2)^3 \\\\ = -\dfrac{5}{6}(-8) \\\\= -\dfrac{-40}{6} \\\\= \dfrac{20}{3}\\\\ = 6.6667 [/tex]

So, the coordinates of the points are:

A: [tex](2, -6.6667)[/tex]

B: [tex](-2, 6.6667)[/tex]

These points indeed fall within the given grid.