Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
- No direct alignment recorded
New NZC (2026)
NZC26-P4-ALG-ER-P-Y10-05
Resources
- Kuta Software - Graphing Rational Functions (asymptotes, discontinuities, intercepts)Questions PDF · Answers
- Dr Austin Maths - Sketching Reciprocal Graphs Practice GridQuestions PDF · Answers
Terminology
- Rational function
- Vertical asymptote
- Horizontal asymptote
- Rectangular hyperbola
- Reciprocal function
- x-intercept
- y-intercept
- Algebraic division
Task goals
- Foundation: Identify the vertical asymptote (where cx+d=0) and horizontal asymptote (y=a/c) of a given function of the form (ax+b)/(cx+d) by inspection.
- Proficient: Rewrite (ax+b)/(cx+d) in transformed reciprocal form k/(x-h)+v via algebraic division, then sketch the full graph showing asymptotes, x- and y-intercepts, and correct branch orientation.
- Excellence: Use the graph or algebraic form of a linear-over-linear rational function to solve related equations or inequalities, or to determine the function's equation from given asymptotes and an intercept.
Where this fits
What leads into this objective, and where it goes next.
Before
Forming equations of given straight line graph (using y=mx+c)
Sketching a Straight Line from Its Equation
Finding x- and y-intercepts
You are here
Graphing Rational Functions / Rectangular Hyperbolae of the Form (ax+b)/(cx+d)
Next
Year 10 is the last year of this phase — the curriculum lists nothing after this. No extension resources on the site yet.
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.