Hey there! Let's talk about whether the function h(x) = x + 5/7 is linear or nonlinear. Imagine you have a magic box called a function that takes a number as an input and gives you another number as an output. In this case, the function is like a toy that adds 5/7 to any number you put inside it.
Now, let's play a game with our function. If you put the number 0 inside the function, it works its magic and gives you the number 5/7 as the output. Then, if you put the number 1 inside, the function gives you 1 + 5/7 as the output, which is 12/7. You can keep trying different numbers like 2, 3, or even fractions like 1/2 to see how the function changes the input number.
A function is linear if it follows a specific pattern: when you increase the input by a certain amount, the output also increases by a consistent amount. In our case, when you increase x by 1, the output increases by 1, and an additional 5/7. It stays consistent every time, like a robot that always adds the same number. This pattern tells us that the function h(x) = x + 5/7 is a linear function.
In contrast, a nonlinear function would be like a mischievous cat that changes its behavior unpredictably. For example, if the function gave you a different result each time you put in the same number, it would be nonlinear. But our function h(x) behaves nicely and predictably, so it falls into the linear category. Hopefully, this explanation helps make it easier to understand whether h(x) = x + 5/7 is linear or nonlinear!