Transformations of graphs
Adding a constant to a function shifts its graph: f(x) + k moves it up or down by k, while f(x + k) moves it left or right; for example, if f(x) = x^2, then f(x) + 3 shifts the parabola up 3 units. Multiplying by a constant stretches or compresses it: k times f(x) stretches the graph vertically, while f(kx) stretches or compresses it horizontally, and a negative k also flips the graph. A function is even if its graph is symmetric about the y-axis (f(-x) = f(x)) and odd if it's symmetric about the origin (f(-x) = -f(x)), which you can recognize from either its graph or its algebraic expression.
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