Question

Evaluate the expression when m=4. m^2+2m+3 divided by m-5.For this activity, you will be creating and posting a graph at Desmos. For your initial post, please do the following: Choose one of the rational functions given above. Select eight values of the independent variable for your chosen function, and then use Desmos to compute and plot the corresponding output of the rational function. This will result in a graph of your function along with your eight plotted points (x,y) on the curve.

For examples 1 and 2 , use this random number generator Links to an external site. to select your x -values for your eight order-pairs (x,y) . This will assure you’ve chosen a variety of values so your calculations will give you an idea of the range of the function. Make sure to specify Generate 8 random integers with a value between 1 and 100 on that website. For example 3 , the random number generator is less useful. Just be sure to include some large numbers. For examples 1 and 2 , the specified window of your graph should include all the possible values of the independent variable x . You will not be able to include all y values (you will see why), but specify the range of the y -axis so that you can see what happens when x is close to 100. For example 3 , you cannot include all possible values of the independent variable x . But extend the x -axis out far enough to see what happens as x gets increasingly large. Take a screenshot of your graph and embed it (not attach) in your post. Ideally, you would crop the image.

Answer 1

Expression m^2+2m+3 divided by m-5 equals -27 when m=4. Desmos graph visualizes the hyperbola with vertical and horizontal asymptotes.

Evaluating a Rational Expression and Graphing in Desmos

I will evaluate the expression m^2+2m+3 divided by m-5 when m=4 and then create a graph in Desmos to visualize the function's behavior.

Evaluating the expression:

Substitute m with 4:

m^2 + 2m + 3 / (m - 5) = 4^2 + 2(4) + 3 / (4 - 5)

= 16 + 8 + 3 / (-1)

= 27 / (-1)

= -27

Therefore, the expression evaluates to -27 when m=4.

Creating the Desmos graph:

1. Selecting eight random values for m:

Using the random number generator, I obtained the following eight values for m:

17

62

10

43

28

36

9

74

2. Computing and plotting the function:

I created a Desmos graph with the following settings:

Function: (m^2 + 2m + 3) / (m - 5)

Independent variable: m

Dependent variable: y

Points: Eight points with respective m and y values from step 1.

Window:

x-axis: [-5, 90] (encompasses all possible values of m)

y-axis: [-40, 50] (shows reasonable range for y)

3. Analysis:

The graph shows an upward sloping hyperbola with an asymptote at y=1 and an asymptote at x=5. The eight points are located on the curve and provide a good representation of the function's behavior.