# Quick Access

# Introduction

Just like transformations in geometry, we can translate/shift a mathematical object by changing its function.

Already seen with the previous models (linear, quadratic), **we can
move it up or down by adding a constant to the function**:

$$f(x) → f(x) + b$$

**To move it left or right, we add a constant to the function variable (x-value)**:

$$f(x) → f(x + a)$$
We can think of this as moving the "abscissa origin" to be more in advance or a bit late.

Putting it together:

$$\textbf{f(x) → f(x + a) + b}$$

Why adding a positive number a to the variable does move the function to the left (the negative direction)?

Well imagine you want to start recording a movie at 8:00 with the function:

Start(t) = 8:00 o’clock.

If you change your mind to say that we want to record 5 minutes before, we will have the function:

Start(t + 5 mins) = 8:00 o’clock

Adding 5 minutes to the current time will make the record starting 5 minutes earlier
(i.e. to the left direction).
It is just like putting our watch in advance for an appointment.