Why does the translation y=f(x+2) translate the graph f(x) 2 units left instead of 2 to the right?

It seems like f(x+2) should translate the graph y=f(x) 2 to the right, it is +2 inside the bracket after all? However, if we think of the translation as actually subbing in x+2 into the equation y=f(x), it may become more intuitive. For example, take f(x)=x2, this will give f(x+2)=(x+2)2. Look at when x2=0 and when (x+2)2=0. This will happen at x=0 and x=-2 respectively. Subsequently, the point (0,0) from (x,f(x)) has become (-2,0) in (x,f(x+2)). This means it has been moved 2 to the left. More generally, if we thing of any point on the graph y=f(x), the translation of f(x+2) will take values of f(x) that are 2 to the right of it. This will make y=f(x+2) 2 units left of the y=f(x).

SH
Answered by Seth H. Maths tutor

9500 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve: 3^(x^2-5x+2)=9^(x+1)


Solve for x 2x +3 + (4x-1)/2 = 10


How would I make S the subject of the formula in the equation V^2 = U^2 + 2AS


The difference between two positive numbers is 50. The second number is 50 % smaller than the first one. What are the two numbers?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning