Evaluate and join a piecewise function

Practise evaluate and join a piecewise function with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Let $f(x)=x+2$ for $x<1$, and $f(x)=kx^2+1$ for $x\geq1$. (a) Find k so f is continuous at $x=1$. [2 marks] (b) For this k, find $f(0)$ and $f(2)$. [2 marks]

Worked explanation

• Part (a)

  The left-hand limit is $1+2=3$. The right branch has value $k+1$ at 1, so continuity requires $k+1=3$.

• Part (b)

  Zero uses the first rule: $0+2=2$. Two uses the second: $2(2^2)+1=9$.

(a) $k=2$.; (b) $2$ and $9$.

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