A common analogy used as an intuitive explanation for a Maclaurin series is that of a car. If you know the position, velocity, acceleration, jerk etc. of a car at time zero, you are able to predict its position at any time after that moment. Simarly, a Maclaurin has the same derivative, second derivative etc. as the function, which is why it approximates the function and can be used to find the range value of a function at any domain value.
Knowing the position, velocity, acceleration, jerk etc. of a car at time zero allows you to figure out its position at any time after time zero. It tells you nothing about its position before time zero. Similarity, shouldn't a Maclaurin series approximate a function for all $x > 0$? Why does it approximate the function for negative domain values?
I would appreciate it if answers made reference to the analogy of the car. Thank you.