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Question

A function f is one-to- one of different inputs produce (the same, different, negative, or positive) outputs? You can tell from the graph that a function is one-to-one by using the (Curved line, Inverse function, Horizontal line, or Vertical line) ?

Answer 1

When describing a function as "one-to-one" it implies that the all inputs to the function produce unique outputs. Every value in the domain of the function will be mapped to a different value in the function's range.

To determine if a single variable function is one-to-one, we can plot the function with inputs along the horizontal axis and outputs along vertical axis. We can then move an imaginary horizontal line over the range of outputs and ask the question: Does the line intersect the plot of the function more than once?

1. If the answer is yes then the function fails the horizontal line test and is not one-to-one.
2. If the answer is no then the function passes the horizontal line test and the function is one-to-one (at least over the domain that the plot spans).

I hope this helps!