AC9M10A05

experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns

Elaborations

AC9M10A05_E1 - applying 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_E2 - applying 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_E3 - applying transformations to the graph of \(x^2+y^2=1\)
AC9M10A05_E4 - identifying 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_E5 - identifying intervals on the real number line over which a given quadratic function is positive or negative
AC9M10A05_E6 - using 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

Achievement Standard Components

ASMAT1003 - Students make and test conjectures involving functions and relations using digital tools.