Knowing the graphs of "parent functions", such as f(x) = x^2 and f(x) = |x| makes it simple to graph variations of such functions.

For example,

f(x) = |x| + 3 has the same graph as f(x) = |x| except it's translated 3 units up. Similarly f(x) = |x| - 3 would be the same as f(x) = |x| except it is translated 3 units down.

For f(x) = (x - 3)^2, the graph is the same as for f(x) = x^2 except it is translated 3 units to the right. Similarly, f(x) = (x + 3)^2 has the same graph as f(x) = x^2 except it is translated 3 units to the left.

You can also have translations horizontally and vertically in the same function

f(x) = (x + 4)^2 - 3 is translated 4 units left and 3 units down from the graph of f(x) = x^2

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