CCSS HSF-IF.C.7.d Worksheets
Algebra 2 · Interpreting Functions
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behaviour, including any holes left by a cancelled common factor.
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Teaching guide
What students learn
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behaviour, including any holes left by a cancelled common factor.
Worked example
For f(x) = 3/(x + 1), state the vertical asymptote(s), horizontal asymptote, any holes and the x-intercept(s), then sketch the graph.
Answer: Vertical asymptote: x = -1; Horizontal asymptote: y = 0; No holes; No x-intercept
Why: Factor: the denominator is zero at x = -1 (the vertical asymptote). For end behaviour, the numerator degree is less than the denominator degree, so the horizontal asymptote is y = 0. The numerator is zero at no value in the domain (the x-intercepts).
Generated and checked in code, so it is correct.
Algebra worksheets
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