Mathematics — first biennium · Lesson
In y=a/(x−h)+k, x=h is excluded from the domain and is the vertical asymptote; y=k is the horizontal asymptote.
Prerequisites: Inverse proportionality and fraction domain
Goal: Interpret domain, asymptotes and translations of a simple reciprocal function.
In this lesson: Interpret domain, asymptotes and translations of a simple reciprocal function.
New concept: An asymptote is a line that the graph approaches more and more closely. In y=a/(x−h)+k, x=h is the vertical asymptote and an excluded domain value; y=k is the horizontal asymptote.
How to proceed: First find where the denominator is zero; then read the vertical shift k.
You can already assume: Inverse proportionality and fraction domain.
Change a, h and k to see how both branches change and how the asymptotes x = h and y = k move.
With a = 0 the curve loses this family's characteristic shape; also try a non-zero value.
The dashed lines show the asymptotes: the two branches approach them without reaching them.
Completed exercises: 0/5 · Correct on first attempt: 0
First find where the denominator is zero; then read the vertical shift k.
Data / situation: y=-1/(x+2)−2
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.