# A certain country taxes the first $19,000 of an individual's income at a rate of 15%, and all income over $19,000 is taxed at 25%. How do you find a piecewise-defined function T that specifies the total tax on an income of x dollars?

##### 1 Answer

Feb 12, 2018

See a solution process below:

#### Explanation:

First, let's call the individual's income:

Let's call the amount of tax they will pay:

"Percent" or "%" means "out of 100" or "per 100",

Therefore, 15% can be written as

And, 25% can be written as

Then if, the individuals income is less than or equal to $19,000 the amount of tax they will pay in terms of

The amount of tax they will pay if they earn more than $19,000 is:

The piece wise function would be: