Question

(a) What is a one-to-one function?

(b) How can you tell from the graph of a function whether it is one-to-one?

Short answer

a. A one-to-one function never takes two similar values.

b. Horizontal line test is used to quantify from the graph of a one-to-one function.

Step-by-step solution

(a) Write the definition of one to one function

A function that never takes the same value twice in its domain is a one-to-one function. For a function \(y = f\left( x \right)\), if \({x_1}\) and \({x_2}\) are in its domain, then

\(f\left( {{x_1}} \right) \ne f\left( {{x_2}} \right)\)

(b) Write solution for part (b)

Using the horizontal line test, the function can be categorized as the one-to-one function or some other function.

The test is done by drawing a horizontal line, and if the line intersects the graph only once, then the function is a one-to-one function.