Can a Decreasing Function Connect These Two Points? Graph Challenge

Copy the points and complete the graph of the function according to the instructions, if it is not possible explain why.

Is it possible to generate a decreasing function with the two given points?

To determine if a decreasing function is possible with the two given points, we need to calculate the slope between them based on the common definition of a decreasing function.

Let's follow these steps:

• Step 1: Identify the given points.
• Step 2: Calculate the slope using these points.
• Step 3: Verify that the slope is negative.

Step 1: The points appear to be roughly at coordinates near $(x_1, y_1)$ and $(x_2, y_2)$ according to their positions on the graph, with exact coordinates not provided, we'll assume accurate readings from the visual information.

Step 2: Calculate the slope using the formula:

$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$

Given the visual interpretation:

$x_1 < x_2$ and $y_1 > y_2$, so this ensures the change in $y$ is negative when divided by a positive change in $x$.

Step 3: As the slope $\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$ is negative, the function represented by these points is decreasing.

Therefore, it is POSSIBLE to generate a decreasing function with the two given points.