I'm currently enrolled in College Algebra, and it is possible that I'm making too much out this; however, this is bugging me a bit and I can't quite get my head around it. I understand(adsbygoogle = window.adsbygoogle || []).push({}); howto perform the various shifts and stretches of the graph of a function, but I'm trying to reach a better conceptual understanding of what the different effects are.

Horizontal shifts are baffling me a bit. For example, I understand that f(x) = (x-2)^2 is going to shift the parabola to the right. What I can't quite put my finger on iswhy? I'm not even sure if that question makes any sense, nor am I sure why this is sticking with me like this. Perhaps it's because it seems contrary to what it appears to do at first glance. A vertical shift f(x) = x^2 + c, with the constant outside the grouping symbols, is going to very obviously shift the graph of the function up (if c > 0) or down (if c < 0). That makes sense to me.

I can plug numbers in for x in f(x) = (x-2)^2, and I can observe the results, but the reasoning or logic behind it eludes me.

Any help here? Am I even making any sense? Am I over-analyzing a basic College Algebra class? I'm studying the material a great deal in an attempt to really understand the concepts rather than just memorizing the formulas, but I'll admit that I might be going overboard a bit...

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# Homework Help: Horizontal Shift of a function

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