VC2M9A07
experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns
Elaborations
-
investigating transformations of the graph of y=x to the graph of y=ax+b by systematic variation of a and b and interpreting the effects of these transformations using digital tools; for example,
y=x→y=2x (vertical enlargement as a>1) →y=2x-1 (vertical translation) and
y=x→y=12x (vertical compression as 0<a<1) →y=-12x (reflection in the horizontal axis) →y=-12x+3 (vertical translation)
-
investigating transformations of the parabola y=x2 to the graph of y=ax-h2+b in the Cartesian plane using digital tools to determine the relationship between graphical and algebraic representations of quadratic functions, including the completed square form; for example,
y=x2→y=13x2 (vertical compression as 0<a<1) →y=13(x-5)2 (horizontal translation) →y=13(x-5)2+7 (vertical translation) or
y=x2→y=2x2 (vertical enlargement as a>1) →y=-2x2 (reflection in the horizontal axis) →y=-2(x+6)2 (horizontal translation) →y=-2x+62+10 (vertical translation)
-
experimenting with digital tools by applying transformations to the graphs of functions, such as reciprocal y=1x, square root y=x, cubic y=x3 and exponential functions y=2x, y=(12)x, identifying patterns
VC2M9A07 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra