Question

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

Answer 1

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`

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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`