Domain and rangeIB MYP Maths Extended: Mind map

Exam questions on Domain and range

1. A function is defined by $f(x)=2x-3$, where $x$ is a real number and $-1\leq x\leq4$.
   The domain of $f$ is restricted so that $f(x)\geq0$. Find the new domain.2 marks
2. Consider the functions $h(x)=\sqrt{x+3}$ and $k(x)=\dfrac{4}{x-5}$. Each function has the largest possible domain of real numbers.
   State the range of $h$ and give a reason.2 marks
3. A quadratic function is defined by $f(x)=x^2-6x+5$.
   By completing the square, find the coordinates of the lowest point of the graph, and hence state the range of $f$ when its domain is all real numbers.3 marks