1 of 8 0-day streak

Evaluate limits and test continuity

Question 1 of 8

No calculator

Distinguish nearby function values from the value at the input itself

f(x)=\begin{cases}-x-6,&x<-2\\-2x-8,&x>-2\\-4,&x=-2\end{cases}

The third branch defines the value at the join. The nearby left and right branches use strict inequalities

(a)3 marks

Enter the exact left limit, right limit and any requested function value. A nearby branch value and the value at the join are different questions

\(\lim_{x\to-2^-}f(x)\) \(\lim_{x\to-2^+}f(x)\) \(f(-2)\)

(b)1 mark

Choose the justified continuity verdict at the join

Not continuous: both one-sided limits equal \(-4\), but the function is undefined at the input

Not continuous: the left limit \(-4\) and right limit \(-4\) are different

Not continuous: both one-sided limits equal \(-4\), but the defined function value is different

Continuous: both one-sided limits and the function value equal \(-4\)

Give the finite two-sided limit, independently of the point value

Exact finite value