| Written description | Equation change | Example from (x^2) | |---------------------|----------------|----------------------| | Shift right (h) | (f(x-h)) | ((x-3)^2) | | Shift left (h) | (f(x+h)) | ((x+2)^2) | | Shift up (k) | (f(x) + k) | (x^2 + 4) | | Shift down (k) | (f(x) - k) | (x^2 - 1) | | Reflect over x-axis | (-f(x)) | (-x^2) | | Reflect over y-axis | (f(-x)) | ((-x)^2 = x^2) (same here) | | Vertical stretch by (a) | (a \cdot f(x)) | (3x^2) | | Vertical compression by (a) | (a \cdot f(x)) with (0<a<1) | (\frac12x^2) |
Copying answer keys without understanding will hurt you on tests. Use the key to check, then rework incorrect problems. 2-6 practice families of functions form k answer key
Linear Functions: The equation is f(x) = x. The graph is a straight line passing through the origin at a 45-degree angle.Absolute Value Functions: The equation is f(x) = |x|. The graph forms a distinct V-shape with the vertex at (0,0).Quadratic Functions: The equation is f(x) = x squared. This creates a U-shaped curve known as a parabola.Constant Functions: The equation is f(x) = c. This results in a horizontal line where the y-value never changes. Vertical and Horizontal Translations | Written description | Equation change | Example
Every complex equation starts with a simple parent function. On Form K, you will likely encounter these four primary types: The graph is a straight line passing through
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