Learning Resources

Investigation 2: Graphs of Quadratic Functions and Their Reciprocals

f(x) = x² -1 and

• The zeros of f(x) correspond to the vertical asymptotes of . What are the equations of these asymptotes?
• Large absolute values of f(x) correspond to small absolute values of , and vice versa.
• The graphs of f(x) and intersect when y = 1.
• Why does the value of g(x) change sign at each asymptote? Why wasn't this the case for the pair of functions y = x² and ?
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Given f(x) = x² + 1 and

• Why is it that the graph of g(x) has no vertical asymptotes?
• At what y-value do the two graphs intersect?
• When the absolute-value of f(x) becomes large, what happens to the corresponding absolute-value of ?