11.3 Functions

Functions

1. 1. Understand the definition of a function and a relation; use domain and range.
2. 2. Apply the vertical line test to determine whether a relation is a function.
3. 3. Use function notation: evaluate $f(a)$, solve $f(x) = k$, and interpret in context.
4. 4. Find the largest natural domain of a real-valued function involving fractions and square roots.
5. 5. Determine inverse functions both algebraically and graphically.
6. 6. Use composite functions with $f \circ g$ notation; find the domain of a composition.
7. 7. Recognise and sketch absolute-value and step functions.
8. 8. Explore Euler's number $e$ and the function $e^x$.