Curve-Sketching Supplement: For each of the following functions, do the following: a) Find the roots (if any). b) Find the vertical, horizontal, and slanted asymptotes (if any). c) Find the critical points (if any). Determine which are local maxima/minima. d) Find the possible points of inflection (if any). Determine which are points of inflection. e) Identify where the function is positive/negative, increasing/decreasing, and concave up/concave down. f) Sketch a graph of the function.

𝑥 2 +1

1. 𝑓(𝑥) = 𝑥 2 −4

2. 𝑔(𝑥) =

2𝑥 2 −5𝑥+5 𝑥−2

8

3. ℎ(𝑥) = 𝑥 − 𝑥 2 4. 𝑘(𝑥) = 𝑥√9 − 𝑥 2 5. 𝑚(𝑥) = 3𝑥 2/3 − 2𝑥 6. 𝑝(𝑥) = 3𝑥 4 + 4𝑥 3 7. 𝑞(𝑥) = 𝑥 1/3 (𝑥 + 3)2/3 1 4

8. 𝑟(𝑥) = cos 𝑥 − cos(2𝑥) when 0 ≤ 𝑥 ≤ 2𝜋

9. 𝑠(𝑥) = 𝑥 tan 𝑥 when −

10. 𝑡(𝑥) = |𝑥 3 − 6𝑥 + 5|

3𝜋 2

≤𝑥≤

3𝜋 2