Chapter 4.1, Problem 1E

To determine

To check:

Whether the given function is one-to-one.

Answer to Problem 1E

Solution:

Yes. The function is a one-to-one function.

Explanation of Solution

In a one-to-one function, each value corresponds to only one $y$ value. And each $y$ value corresponds to only one $x$ value.

A function $f$ is a one-to-one function if, for elements $a$ and $b$ in the domain of $f$,

$a\ne b$ implies $f\left(a\right)\ne f\left(b\right)$.

Calculation:

The following table shows the number of registered passenger cars in the United States for the years 2004-2008.

Year	Registered Passenger Car (in thousands)
2004	136, 431
2005	136, 568
2006	135, 400
2007	135, 933
2008	137, 080

If this correspondence is considered to be a function that pairs each year with the number of registered passenger cars, we need to find whether is it one-to-one function.

In the given table, let $x$ represents the year and $y$ represents the registered passenger cars (in thousands).

From the given table, we find that the all the $x$ values correspond to only one value and the $y$ values are not repeated for any value of $x$. Hence, the function is a one-to-one function.

Thus, the function is a one-to-one function.

Final statement:

Yes. The function is a one-to-one function.