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Unformatted text preview: 02)
30002 (−1.001, 30002) x
−0.9999 f (x)
(x, f (x))
−29998 (−0.9999, −29998) As the x values approach −1 from the left, the function values become larger and larger positive
numbers.2 We express this symbolically by stating as x → −1− , f (x) → ∞. Similarly, using
analogous notation, we conclude from the table that as x → −1+ , f (x) → −∞. For this type of
unbounded behavior, we say the graph of y = f (x) has a vertical asymptote of x = −1. Roughly
speaking, this means that near x = −1, the graph looks very much like the vertical line x = −1.
Another feature worthy of note about the graph of y = f (x) is it seems to ‘level oﬀ’ on the left and
right hand sides of the screen. This is a statement about the end behavior of the function. As we
discussed in Section 3.1, the end behavior of a function is its behavior as x as x attains larger3 and
larger negative values without b...
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