A function is a set of rules so that for every input, we get only one output. We represent functions in math as equations with two variables: x and y. The x is the input and y is the output. For every x we plug into the equation, we only get one y.
We can represent functions on a graph using the coordinate plane with our coordinates being x (the input) and y (the output) in the same way as we graphed things before, with our point (x, y). The functions we’ll see in the videos create a pattern of points that make a line.
Video Source (04:56 mins) | Transcript
In the previous video, we plotted some points from the function and then connected those points with a line. We do this when we have continuous data. If we were to choose any number between the points we plotted, the equation’s output would be on the line because of the pattern the function makes.
Sometimes we plot points that don’t make a perfect pattern or that have no values in between. This is called discrete data and we don’t connect the dots with a line. They just stay as a scatter plot.
Video Source (04:40 mins) | Transcript
A discrete graph is one with scattered points. They may or may not show a direction or trend. They don’t have data in between the points already given.
A continuous graph has a line because there is data in between the points already given.
- Khan Academy: Graphing a Linear Equation: y = 2x + 7 (13:09 mins, Transcript)
Practice Problems1. Is the graph below discrete or continuous?
3. A chicken breeder sells pullets (young hens that have just started laying eggs) for \($25\) each. The breeder charges an additional \($100\) to deliver the animals, regardless of the number purchased. If we let P represent the number of pullets sold, then we can represent the total cost (T) as \(T = 100 + 25P\). Create a graph that illustrates the relationship between P and T, assuming that the number of pullets purchased is between 1 and 8.(Hint: Use the equation for the total cost. Create a table with input values from 1 to 8, and calculate the outputs to find the coordinates that you need to graph.) (
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