We have already done horizontal and vertical translations for trig families, and algebraic families are very similar. Vertical translations are found at the end of the equation, not next to the x, and tell us which way to go on the y-axis. The three functions below are examples of vertical translations:
y = x - 3
y = x^2 + 4
y = 3^x - 1
Horizontal translations are found either inside the parenthesis or, in radical equations, underneath the radical. They tell us where to move on the x-axis, BUT we have to write it backwards in the equation.
For example, if we wanted to do a horizontal translation of +4, we could write:
y = (x - 4)^2 because we would have to write it BACKWARDS.
Note that when we actually graph the equation, we still want to move +4 on the x-axis. We only write it backwards in the equation.
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