AP Precalculus Unit 1 Concept Review

What does "x increases without bound" mean?

• x → 0

• x → ∞

• x → -∞

• x>0

What do "input" and "output" stand for?

• input is y

  output is x

• input is x

  output is y

• both input and output are x

• both input and output are y

When x increases without bound, f(x) decreases without bound.

When you need to sketch the graph of a polynomial function,

which two factors do you need to consider?

画多项式图像的时候，需要考虑哪两个因素？

• end behavior and zeros

• continuity and differentiability

• domain and range

• real zeros and complex zeros

When analyzing the end - behavior of a polynomial function,

which term needs to be considered?

讨论多项式的 end behavior (左右两边) 时，需要考虑哪一项？

• the constant term

  常数项

• the term with the second - highest degree

  次方第二高的项

• the term with the smallest non - zero coefficient

  系数为最小正数的项

• the leading term

  次方最高的项

• ↖ ... ↗

• ↙ ... ↘

• ↖ ... ↘

• ↙ ... ↗

• As x→+∞, f(x)→+∞;

  as x→−∞, f(x)→−∞

• As x→+∞, f(x)→−∞;

  as x→−∞, f(x)→+∞

• As x→+∞, f(x)→+∞;

  as x→−∞, f(x)→+∞

• As x→+∞, f(x)→−∞;

  as x→−∞, f(x)→−∞

Which polynomial function has the end - behavior:

as x→+∞, y→+∞ and as x→−∞, y→+∞?

画 polynomial function 图像时，需要判断 zeros 是否穿过 x 轴。

口诀是什么？

• 奇穿偶不穿

• 偶穿奇不穿

• 正穿负不穿

• 负穿正不穿