Asymptote — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
A line the graph approaches but never reaches — here, the x-axis.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
Practise this idea
2 questions in the course bank use Asymptote, in Exponential Functions & Growth, Rational Expressions & Equations.
Problem 1
As x grows without bound, the graph of y = 3(0.5)x
- approaches 0 but never reaches it
- increases without bound
- becomes negative
- reaches 0 exactly
Worked answer
approaches 0 but never reaches it
Each step halves the value
It gets arbitrarily small
The x-axis is an asymptote
Problem 2
What is the vertical asymptote of y=x+1x-5?
- x=5
- x=-1
- y=5
- y=1
Worked answer
x=5
x-5=0 at x=5
The top is not zero there, so it is an asymptote