#include <iostream>

// A piecewise-defined function uses different formulas
// for different values of its argument.
//
// Consider the following "tent" function:
//
//                 /   0,             x <= -1,
//                 |
//                 | x + 1,      -1 < x <= 0,
//     tent(x) =  <
//                 | 1 - x,       0 < x <= 1,
//                 |
//                 \   0,              1 < x.
//
// Its graph looks like a tent:
//
//
//                           |
//                         1 +
//                          /|\
//                         / | \
//                        /  |  \
//                       /   |   \
//     _________________/    |    \_________________
//                     -1    0     1
//                          |
//
//
// Notice that the function has four different portions:
//
//     1. If x <= -1, the value is 0.
//
//     2. If -1 < x <= 0, the value is x + 1.
//
//     3. If 0 < x <= 1, the value is 1 - x.
//
//     4. If x > 1, the value is 0.
//
// For example:
//
//     x = -2.0    ->    tent(x) = 0
//     x = -1.0    ->    tent(x) = 0
//     x = -0.7    ->    tent(x) = 0.3
//     x =  0.0    ->    tent(x) = 1
//     x =  0.4    ->    tent(x) = 0.6
//     x =  1.0    ->    tent(x) = 0
//     x =  1.8    ->    tent(x) = 0
//
// Write a program that asks the user for a value of 'x'
// and then evaluates and prints tent(x).
//
// A cascading conditional statement is particularly
// useful for implementing a piecewise-defined function.

// Function declarations
int main();

// Function definitions
int main() {
    double x{};

    std::cout << "Enter a number 'x': ";
    std::cin >> x;

    if ( x <= -1.0 ) {
        // We know that
        //
        //     x <= -1,
        //
        // so tent(x) = 0.

        std::cout << "tent(x) = " << 0.0 << std::endl;
    } else if ( x <= 0.0 ) {
        // The first condition was false, so we already
        // know that
        //
        //     x > -1.
        //
        // Together with the current condition, we know
        //
        //     -1 < x <= 0.
        //
        // Thus, tent(x) = x + 1.

        std::cout << "tent(x) = " << (x + 1.0) << std::endl;
    } else if ( x <= 1.0 ) {
        // The first two conditions were false, so we
        // already know that
        //
        //     x > 0.
        //
        // Together with the current condition, we know
        //
        //     0 < x <= 1.
        //
        // Thus, tent(x) = 1 - x.

        std::cout << "tent(x) = " << (1.0 - x) << std::endl;
    } else {
        // All three conditions were false, so we know
        //
        //     x > 1.
        //
        // Thus, tent(x) = 0.

        std::cout << "tent(x) = " << 0.0 << std::endl;
    }

    return 0;
}