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=xto 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=x2to 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 functionsy=2x,y=(12)x, identifying patterns
Code
VC2M9A07
Curriculum resources and support
Find related teaching and learning resources in
Arc*
