![]() ![]() This means the graph doesn’t have any waves so it passes the horizontal line test and is one-to-one. Examples Example 1Ī very similar example to earlier! Yet again, you’ve got a transformation of a familiar function.Īs you move from left to right, the function is always decreasing. Some resources, like Desmos, will let you slide a horizontal line across graphs! It’s a fantastic way to visualize it. The test also works on computers! Either hold a straight edge up to the screen or imagine a sliding horizontal line. If there are no more changes of direction, then you can stop there. End behavior and asymptotes – where the graph will continue to and where it never reaches.Maximum and minimum points – where the graph changes direction from increasing to decreasing, or the other way.All x- and y-intercepts – where the graph crosses the axes.The important features top include in your graph are: If you’ve found a position where a horizontal line intersects the graph at more than one point, draw it on!.Draw some evenly spaced horizontal lines to demonstrate your result. If there aren’t any horizontal lines that would intersect the graph in more than one place, you’re done.Are there any positions where the edge of the ruler intersects the graph at more than one point? Hold a ruler horizontally – remember horizon! – across the graph and move it up and down.Get a suitably zoomed-out copy of your graph, showing all the important features of its shape.Remember that each input must have only one output to be an official function. You might come across one-to-many or many-to-many relations but, strictly speaking, these aren’t functions. It would be difficult to cook with an oven which gives different food from the same ingredients! You want to be certain what food your oven makes, so you want a clear output. It’s like your cake recipe: there are lots of ways to make the cake mix, but some of them give the same delicious result! One input is converted to one output.įunctions can also be many-to-one, where several inputs have the same single output. If each specific input corresponds to a single specific output, the function is one-to-one. Think of functions as ovens: put in food, and they give you a cooked meal! Give them an input, and they give you an output. Read on, and you’ll only be passing your next math test! One-to-One Functionįunctions are math machines. It’s called a test because just like a math test, there are two outcomes! A function can either pass or fail, depending on its shape. What’s in a name? A horizontal line goes left to right across a page, like the horizon does on a nice sunny beach. To Sum Up (Pun Intended!) Horizontal Line on a Graph ![]()
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