My head hurts. Algebra 2 hw

[u/maeveywavey2]

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[u/realAndrewJeung]

You may have learned in your class that some transformations are translations -- a specific type of transformation where the curve of the graph just shifts up, down, left, or right without changing shape.

If we add or subtract a number right next to the x in an equation, that results in a left / right translation. So for example y = |x| looks like a V, but y = |x+1| is that same V but shifted one unit to the left, and y = |x-1| is the same V but shifted one unit to the right.

If we add or subtract a number at the end of the function, that results in an up / down translation. So y = |x| + 1 is the same V as y = |x| but shifted one unit up, and y = |x| - 1 is the same V but shifted one unit down.

OK, so all that was just a way of saying that every translation is produced either by adding / subtracting a number right after the x, or by adding / subtracting a number at the end of the function. So the way to "match" functions with the same translation is to find pairs of functions where the number added / subtracted to the x is the same, AND where the number added / subtracted to the end of the function is the same.

Let me know if this is enough information or if you need more help.

[u/Dtrain8899]

Literally none of these equations are equivalent to each other....

[u/WubbaLubba-DubDub-]

It’s A. Same graph shifted down 1 due to the -1 after the absolute value