Graphing+Linear+Functions-Target+C-Restrict+It-Guided+Learning

Target C: Graph linear functions given a domain and identify the range.

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A graph of a linear function can be considered continuous or discrete depending the DOMAIN of the function.

If the domain of a function is all real numbers, then the graph of the function is continuous.
 * CONTINUOUS**

Example: f(x) = 3x - 1; Domain: the set of all real numbers. In order to graph the function, create a table of values, choose x-values and substitute into the function in order to find the corresponding y-values. The numbers chosen below are {-2, -1, 0, 1}, but any x-values can be used because the domain is all real numbers. The numbers selected for the domain will vary depending on the function (i.e. if the function is y = 1/2x + 4, then the x-values chosen should be multiples of 2, such as -4, -2, 0, 2, 4, in order to eliminate the fraction). Then, plot the coordinates on a graph, and connect to form a continuous line.

In this case, since the domain of the function is all real numbers, then the range of the function is also all real numbers. This will be the case for the majority of linear functions. If the domain is the set of all real numbers, then the range is also the set of all real numbers.


 * There are SPECIAL cases where this does not happen, however, so you always need to make sure to check the graph of the function when determining the range. For example, if we had the function f(x) = 2, then the graph of the line would be a horizontal line passing through (0, 2) on the y-axis. So the range would be {2}, and not all real numbers.**



Domain: All Real numbers

Range: {2}

DISCRETE
 * If the domain of a function is a given set of x-values, then the graph of the function is discrete. Let's take a look using the same function as above.**


 * Example: f(x) = 3x - 1; Domain: {-2, -1, 0, 1}**
 * In order to graph this function, use only the given domain to find the range.**


 * Then, plot the coordinates on a graph, but this time, do not draw a line through the points. The graph of the function is discrete because the graph should only represent the values of the specific domain.**


 * The range of the function would only consist of {-7, -4, -1, 2}.**

Graphing Linear Functions-Target B-Restrict It-Quick Check**

1) Graph the function y = 2x - 1 with domain: {all real numbers}. Identify the range.

2) Graph the function y = 2x - 1 with domain: {-3, -1, 0, 1, 3}. Identify the range.

Graphing Linear Functions-Target B-Restrict It-Quick Check Solutions