Restricted domain and range

Practise restricted domain and range with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Let $f:[-1,4]\to\mathbb R$, $f(x)=(x-2)^2+1$. (a) Find the minimum value and where it occurs. [2 marks] (b) State the range of f. [2 marks]

Worked explanation

• Part (a)

  $(x-2)^2\geq0$, with equality at $x=2$ in the domain. Hence the minimum is $1$.

• Part (b)

  $f(-1)=10$ and $f(4)=5$. The continuous quadratic has its minimum inside the interval and maximum at $-1$, so its range is $[1,10]$.

(a) $1$ at $x=2$.; (b) $[1,10]$.

Original VectorPaths practice; not an official VCAA question or marking rubric.