Mathematics: Applications and Interpretation · Topic 2: Functions

SL2.5 — Modelling with functions

Mathematics: Applications and Interpretation · SL / HL · syllabus-mapped notes

1. AISL2.5.1

   Linear and piecewise linear models

   $f(x)=mx+c$ with $m$ a constant rate of change, and piecewise linear models over intervals.

2. AISL2.5.2

   Quadratic models

   $f(x)=ax^2+bx+c$, $a\neq 0$: axis of symmetry, vertex, zeros and intercepts.

3. AISL2.5.3

   Exponential and variation models

   Exponential growth and decay $f(x)=ka^x+c$ and variation $f(x)=ax^n$, with their asymptotes.

4. AISL2.5.4

   Cubic and sinusoidal models

   $f(x)=ax^3+bx^2+cx+d$ and $f(x)=a\sin(bx)+d$: amplitude, period and principal axis.