Analyze graph transformations caused by f(x)+k, kf(x), f(kx), and f(x+k); identify even/odd functions.
Describe a horizontal shift of a function
Problem
Describe the horizontal shift from \(f(x)\) to \(f(x+3)\).
Big Picture
What this problem is really about
A constant added inside the function changes inputs, so the horizontal direction cannot be read from its visible sign alone. We’ll match a transformed input to an original input, solve for the new x-coordinate, and keep the output unchanged. That point mapping reveals both the shift amount and why inside translations move in the inverse direction.
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