AC9M9A06 Year 9 Mathematics

Content descriptor 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

• • Elaboration investigating transformations of the graph of y=x to the graph of y=ax+b by systematic variation of a and b and interpretating the effects of these transformations using digital tools; for example, y=x\rightarrow y=2x (vertical enlargement as a>1) \rightarrow y=2x-1 (vertical translation) and y=x\rightarrow y=1/2x (vertical compression as a<1) \rightarrow y=-1/2x (reflection in the horizontal axis) \rightarrow y=-1/2x+3 (vertical translation)
• • Elaboration investigating transformations of the parabola y=x^2 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=x^2\rightarrow y=1/3x^2 (vertical compression as a<1) \rightarrow y=1/3(x-5)^2 (horizontal translation) \rightarrow y=1/3(x-5)^2+7 (vertical translation) or y=x^2\rightarrow y=2x^2 (vertical enlargement as a>1) \rightarrow y=-2x^2 (reflection in the horizontal axis) \rightarrow y=-2(x+6)^2 (horizontal translation) \rightarrow y=-2(x+6)^2+10 (vertical translation)
• • Elaboration experimenting with digital tools by applying transformations to the graphs of functions, such as reciprocal y=\frac1x, square root y=\sqrt x, cube y=x^3 and exponential functions, y=2^x, y=(1/2)^x, identifying patterns
• • Elaboration investigating how experimenting with the effects of the variation of parameters of related functions can provide artificial intelligence researchers insights into the predictive behaviour of artificial intelligence models