A1.3

explain the meanings of the terms domain and range, through investigation using numeric, graphical, and algebraic representations of the functions $f(x)=x$, $f(x)=x^2$, $f(x)=\sqrt{x}$, and $f(x)=\frac{1}{x}$; describe the domain and range of a function appropriately (e.g., for $y=x^2+1$, the domain is the set of real numbers, and the range is $y\ge 1$); and explain any restrictions on the domain and range in contexts arising from real-world applications Sample problem: A quadratic function represents the relationship between the height of a ball and the time elapsed since the ball was thrown. What physical factors will restrict the domain and range of the quadratic function?