Answer:

Piecewise functions are functions that have various pieces or "pieces" that are defined over different intervals or domains. In order to understand the use of piecewise functions to solve real-life problems, consider the following steps:

1. Break the problem into separate intervals that will define each piece of the function. In other words, identify the different domains or intervals over which the function is defined.

2. Identify the type of function that would be appropriate for each piece, based on the nature of the problem and the given data. Consider using basic functions such as linear, quadratic, or exponential functions, among others.

3. Translate

Step-by-step explanation:

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Answer:

Piecewise functions involving real-life problems. Piecewise functions are mathematical functions that are defined by different equations or rules for different intervals or "pieces" of the function's domain. They are often used to model real-life situations that have different behaviors or relationships depending on certain conditions or inputs.

Here's an example of a real-life problem involving a piecewise function:

Problem: A transportation company charges different rates for bus tickets based on the age of the passenger. For passengers aged 0-12 years, the ticket price is $5. For passengers aged 13-18 years, the ticket price is $8. For passengers aged 19 and above, the ticket price is $10. Write a piecewise function to represent the ticket price based on the passenger's age.

Solution:

Let's define a function P(x) to represent the ticket price based on the passenger's age (x).

For passengers aged 0-12 years: P(x) = $5

For passengers aged 13-18 years: P(x) = $8

For passengers aged 19 and above: P(x) = $10

In mathematical notation, we can represent this piecewise function as follows:

P(x) = {

$5 if 0 ≤ x ≤ 12,

$8 if 13 ≤ x ≤ 18,

$10 if x ≥ 19

}

The piecewise function P(x) takes in the age of the passenger (x) and returns the corresponding ticket price based on the given conditions.

I hope this example helps illustrate how piecewise functions can be used to model real-life problems.