AC9M9A06

Elaborations

• AC9M9A06_E1investigating 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→y=2x (vertical enlargement as a>1) →y=2x-1 (vertical translation) and y=x→y=1/2x (vertical compression as a<1) →y=-1/2x (reflection in the horizontal axis) →y=-1/2x+3 (vertical translation)
• AC9M9A06_E2investigating 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→y=1/3x^2 (vertical compression as a<1) →y=1/3(x-5)^2 (horizontal translation) →y=1/3(x-5)^2+7 (vertical translation) or y=x^2→y=2x^2 (vertical enlargement as a>1) →y=-2x^2 (reflection in the horizontal axis) →y=-2(x+6)^2 (horizontal translation) →y=-2(x+6)^2+10 (vertical translation)
• AC9M9A06_E3experimenting with digital tools by applying transformations to the graphs of functions, such as reciprocal y=1/x, square root y=√(x), cube y=x^3 and exponential functions, y=2^x, y=(1/2)^x, identifying patterns
• AC9M9A06_E4investigating 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