AC9M10A05

Elaborations

• AC9M10A05_E1applying the graphing zoom functionality of digital tools and systematically refining intervals to identify approximate location of points of intersection of the graphs of 2 functions, such as x^2=2^x
• AC9M10A05_E2applying a bisection algorithm to determine the approximate location of the horizontal axis intercepts of the graph of a quadratic function such as f(x)=2x^2-3x-7
• AC9M10A05_E3applying transformations to the graph of x^2+y^2=1
• AC9M10A05_E4identifying the coordinates of any points of intersection of the graph of a linear function with the graph of a quadratic function or a circle
• AC9M10A05_E5identifying intervals on the real number line over which a given quadratic function is positive or negative
• AC9M10A05_E6using a table of values to determine when an exponential growth or decay function exceeds or falls below a given value, such as monitoring the trend in value of a share price in a context of exponential growth or decay
• AC9M10A05_E7investigating how functions and relations serve as the mathematical underpinnings of machine learning, allowing data to be transformed, models to be defined and optimisation to occur