How do you translate a graph to the left or right?

1 Answer
Oct 25, 2014

When translating a graph to the left or to the right, it means moving the entire graph to the left or to the right of its current location, which is usually relative to #(0, 0 )#

For example, let's say you have a circle centered at #(0, 0)# with radius 2. Its standard equation would be

#x^2 + y^2 = 4#

Now, let's say we translate the circle 5 units to the left. Your circle will now be centered at (-5, 0) with the radius still equal to 2. Its new standard equation would be

#(x + 5)^2 + y^2 = 0#


This is also true for linear equations.
For example, let's say you have a line with slope 1 with the x-intercept equal to 0. Its equation will be

#y = x#

When we translate the line 3 units to the right, its slope will remain the same, but its x-intercept will now be 3. Its new equation will be

#y = x - 5#