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Graphs of Functions (Part 1)

# Graphs of Functions (Part 1) - Domain Recall that the...

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Domain Recall that the domain is the set of all input values to which the rule applies. These are called your independent variables. These are the values that correspond to the first components of the ordered pairs it is associated with. If you need a review on the domain, feel free to go to Tutorial 30: Introduction to Functions. On a graph, the domain corresponds to the horizontal axis. Since that is the case, we need to look to the left and right to see if there are any end points to help us find our domain. If the graph keeps going on and on to the right then the domain is infinity on the right side of the interval. If the graph keeps going on and on to the left then the domain is negative infinity on the left side of the interval. Range Recall that the range is the set of all output values. These are called your dependent variables. These are the values that correspond to the second components of the ordered pairs it is associated with. If you need a review on the range, feel free to go to Tutorial 30: Introduction to Functions. On a graph, the range corresponds to the vertical axis. Since that is the case, we need to look up and down to see if there are any end points to help us find our range. If the graph keeps going up with no endpoint then the range is infinity on the right side of the interval. If the graph keeps going down then the range goes to negative infinity on the left side of the interval. Graphing a Function by Plotting Points Step 1: Find at least four ordered pair solutions.

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Functions can vary on what the graph looks like. So it is good to have a lot of points so that you can get the right shape of the graph, whether it be a straight line, curve, etc.. Step 2: Plot the points found in step 1. Step 3: Draw the graph. Here are the basic shapes of some of the more common graphs of functions. Keep in mind that these are the basic shapes of these graphs. They can be shifted and stretched depending on the function given. A major goal is to recognize what type of function you are graphing and predict the basic shape from that before you even start. Note that the domain and ranges that go with each one are also given. Linear Function
Domain: Range: Constant Function Domain: Range: Quadratic Function

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Domain: Range: Cubic Function
Domain: Range: Square Root Function Domain: Range: Absolute Value Function

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Domain: Range: Example 1 : Graph the function using the given values of x . Also use the graph to determine the domain and range of the function. x = -3, -2, -1, 0, 1, 2, 3 Step 1: Find at least four ordered pair solutions.
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