Give a few examples of scenarios that can be modeled with a linear function. For each scenario, write the function that can model the situation. Then evaluate the function at a given value.

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MAT101 Upload Document: Discussion #3
In the text field below, please provide your response to the following discussion prompt in 250-500 words. Then save the file as either .doc or .docx format, and upload the document into the Upload Area for Discussion 3:

Prompt 1:

Consider an area (yard, living room, park) that you know well. Imagine that a set of x- and y-axes are laid on top of the area. You may choose to orient the axes along the north-south and east-west lines. Write about a walk through the area, detailing your Cartesian coordinate when you are a point of interest.

Example: There is a huge coordinate system in my yard! The x-axis is negative in the west directions and positive in the east direction. North is positive on the y-axis, and south is negative. I begin at the coordinates (0,0), where my kids’ trampoline is. I walk 6 paces west and 12 paces north. My coordinates are now (-6,12)…

Prompt 2:

Give a few examples of scenarios that can be modeled with a linear function. For each scenario, write the function that can model the situation. Then evaluate the function at a given value.

Example : I have a great idea for a zip-line park. Customers pay $10 entry, plus $6 for every zip. The function that models the cost to the customer is:

where z is the number of zips the customer takes.

If a customer takes 7 zips, the cost will be:

Prompt 3:

Consider the piecewise-defined function:

In words, describe your thought process as you evaluate the piecewise-defined function at each of these values of x:

Example for f(4): The value of x is 4, which is greater than -3 and less than 5. Therefore, I will evaluate the second piece of the piecewise-define function. This is the expression 2x + 6. To evaluate, I substitute 4 in for x, which gives 2(4) + 6….

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