mtk
things to do
We’ll start with a simple Logarithm curve. You can investigate the curve as follows:
1. Use the "a" slider to vary the a parameter of the function, and see the effect on the curve.
2. Use the "c" slider to vary the c parameter of the function, and see the effect on the curve.
3. Use the "b" slider to vary the b parameter of the function.
summary
Changing a
Varying a just changes the steepness of the arms of the curve.
Case a > 0: When a is positive, the arms of the parabola point upwards.
Case a = 0: This is a "degenerate" parabola (in this case, a straight line, whose slope depends on the value of b).
Case a < 0: When a is negative, the arms of the parabola point downwards.
Changing b
Case b > 0: The green parabola moves to the left and down (if a is positive) from its "normal" position with the vertex at the origin
Case b = : The green curve does not move around the grey parabola in this case. The vertex will stay at (0, c).
Case b < : The green curve moves to the right and down (if a is positive).
Changing c
Varying c just moves the green parabola up or down.
Case c > : The green curve moves up from its "normal" position with the vertex at the origin.
Case c = : The green curve does not move up or down. The vertex is at (0, 0) (if b = 0).
Case c < : The green curve moves down.