Question

3-16 A function is given by a table of values, a graph, a formula, or a vertical description. Determine whether it is one-to-one.

16. \(f\left( t \right)\)is your height at age \(t\).

Short answer

The function \(f\) is not a one-to-one function

Step-by-step solution

One-to-one function

If a function never takes on the same value again, it is called a one-to-one function. This means that;

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

Determine whether it is a one-to-one function

Because we all stop growing at some stage, the function f is not one-to-one. As a result, there are two instances when we are at the same height.

Thus, the function \(f\) is not a one-to-one function.