AC9M9A06

See also: Learning Areas / Mathematics / Mathematics / Algebra / Year 9

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

• AC9M9A06_E1 - 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 \(y=x\rightarrow y=\frac12x\) (vertical compression as \(a<1\)) \(\rightarrow y=\)-\(\frac12x\) (reflection in the horizontal axis) \(\rightarrow y=\)-\(\frac12x+3\) (vertical translation)
• AC9M9A06_E2 - 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, \(y=x^2\rightarrow y=\frac13x^2\) (vertical compression as \(a<1\)) \(\rightarrow y=\frac13(x-5)^2\) (horizontal translation) \(\rightarrow y=\frac13(x-5)^2+7\) (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)
• AC9M9A06_E3 - 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, \(y=2^x\), \(y=(\frac12)^x\), identifying patterns

Achievement Standard Components

• ASMAT907 - Students describe the effects of variation of parameters on functions and relations, using digital tools, and make connections between their graphical and algebraic representations.