Continuous — Precalculus, what it means and where it is taught
A function you could draw without lifting the pen — no holes, jumps or blow-ups.
Taught in Precalculus.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Function — A rule pairing each input with exactly one output.
Practise this idea
4 questions in the course bank use Continuous, in Sequences, Explicit & Recursive, Parametric Equations, Limits & Continuity.
Problem 1
The graph of a sequence is
- a set of separate points
- a continuous line
- a smooth curve
- a shaded region
Worked answer
a set of separate points
Only the counting numbers
So the graph is separate dots
Never join them
Problem 2
Why can a circle not be written as y=f(x)?
- It fails the vertical line test
- It has no equation
- It is not continuous
- It has no slope
Worked answer
It fails the vertical line test
Two, for most x on a circle
Problem 3
Find limx → 3(2x+1).
Worked answer
7
2(3)+1 = 7
Problem 4
A function has a hole at x=2 but heads for 5 from both sides. Which is true?
- The limit is 5 but it is not continuous there
- It is continuous
- The limit does not exist
- The limit is 0
Worked answer
The limit is 5 but it is not continuous there
The limit exists; the value does not