Function Notation:
- If an equation is written in the form y = mx + c:
- The y can be replaced by f(x) = "eff of x"
- So the new equation would be f(x) = mx + c
- To substitute x = n into the equation:
- EG: If f(x) = 2x² + 1, x = 1: f(1) = 2(1)² + 1 = 3, Therefore: f(1) = 3
Transformation Graphs:
1) y = f(x) + a
- Translation moving in the column vector (0, a).
- Does not change shape.
- Add a to the y coordinates.
- Stretch in the y direction with a scale factor of a.
- Changes shape.
- Multiply the y coordinates by a
- Reflection in the x axis.
- Does not change shape.
- Multiply the x coordinates by -1 or change the signs of x.
- Translation moving in the column vector (-a, 0).
- Does not change shape.
- Subtract a from the x coordinates.
- Stretch in the x direction with a scale factor of 1/a.
- Changes shape.
- Divide the x coordinates by a.
- Reflection in the y axis.
- Does not change shape.
- Multiply the y coordinates by -1 or change the signs of y.