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In order for a graph graph of an equation to be a function it must pass the vertical line test. If it passes the test it means that each x input has a unique y output.
If the shape touches any vertical line more than once it is not a function. Some teachers will call this the "pencil test."
A function will pass the horizontal line test if for each y value (the range) there is only one x value ( the domain) which is the definition of a function.
If a function passes the vertical line test, and the horizontal line test, it is 1 to 1.
Look at the graph below. Notice that graph touches the vertical line at 2 and -2 when it intersects the x axis at 4. Therefore when x = 4 there are two different y-values (2 and -2). For any input x, a function can only have one corresponding y value. So this function FAILS the vertical line test.
The vertical line test, also called a pencil test, is a simple test used to determine if a graph of an equation is a function.
If you draw a vertical line on the coordinate plane where the equation is graphed, and move this line from left to right, it should only touch the graph once, in order for the graph to be a function. ( a pencil works perfect for the vertical line)
If the graph intersects the vertical line more than once, it is not a function, and any x value may have two y values.