A one-to-one graph must pass both the horizontal and the vertical line test. That means that no x-value can have two y-values and no y-value can have two x-values. An example of a one-to-one function is a line. Things like parabolas and the graph of an absolute function cannot be one-to-one.
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If it's one-to-one, and assuming the function is continuous, the function graph must needs be strictly monotonous. That means that, going from left to right, the graph can either ONLY go up, or it can ONLY go down.
A monotonic, or one-to-one function.
A-If there exists a vertical line that intersects the graph at exactly one point, the graph represents a function.B-If there exists a vertical line that intersects the graph at exactly one point, the graph does not represent a function. C-If there exists a vertical line that intersects the graph at more than one point, the graph represents a function.-DIf there exists a vertical line that intersects the graph at more than one point, the graph does not represent a function
A function is just a fancy name for a math problem. It could be a straight line or it could be a parabola or even some thing else. The key to knowing what it looks like is the leading coefficient. What is the highest power of x? Is it positive or negative? An x with the power of one will be a straight line at an angle.
"y = f(x) is a function if it passes the vertical line test. It is a 1-1 function if it passes both the vertical line test and the horizontal line test. " - In order to be a one-to-one function, it first has to BE a function and pass the vertical line test. For example, a relation on a graph like a circle that does not pass the vertical line test is not function nor one-to-one.
if a certain abscissa corresponds to more than one ordinate, then it is not a function.