Today in Precalculus Go over homework Notes: Limits with infinity

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Today in Precalculus Go over homework Notes: Limits with infinity and Asymptotes Homework

Limits and asymptotes The line x = a is a vertical asymptote of the graph of a function y = f(x) if f(x) approaches a limit of +∞ or -∞ from either direction The line y = b is a horizontal asymptote of the graph of a function y = f(x) if f(x) approaches a limit of b as x approaches +∞ or –∞

Infinity as the limit Vertical Asymptote: x = 0 ∞ ∞ ∞

Infinity as the limit VA: x = 2 -∞ ∞ DNE

Limits and Vertical Asymptotes Simplify equation If term in denom goes away, hole at denom = 0 If term does not go away, VA at denom = 0 hole at x = 2 VA: x = -3

Limits with Infinity (end behavior)

Limits with Infinity (end behavior) HA: y = 0 No VA or holes

Limits with Infinity (end behavior) HA: y = 2 2 No VA or holes

Limits with Infinity (end behavior) HA: none ∞ -∞ VA: x=1, x=-1 Holes:none