Ok, let me see if I can clear this up. I'll try to give you the whole nine yards on how to sketch a graph from a function, f.
1) Domain - you just need to figure this by looking at the f function.
2) Intercepts - set 0 to x to find y-int. Set 0 to y to find x-int.
3) Symmetry - odd or even symmetry. Put (-x) in for x. If f(-x) = -f(x) [negation of f], it's odd. If f(-x) = f(x) [the same f], it's even.
4) Asymptotes - take limits of f(x) (original function) to see if they go to + or - infinity. If they both go to different infinities, then it's no horizontal asympt.
5) Intervals of Increasing or Decreasing - Take first derivative. Where f'(x) does not exist (DNE) means cusps or vertical tangents. You need to take lim of f' where x->#DNE. If they both go to different infinities, then it's cusp. Where f'(x) = 0 means it's within domain and you can plug numbers in the f' between critical #'s to see changes in signs. If ---, then f is decreasing, and ++++, then f is increasing.
6) Local Max or Min - the number/s between sign change of the f' determines local max or min of f. So if ---- 7 +++++ means f is decreasing until 7 and increasing after 7. 7 is the local min.
7) Concavity and Inflection Points - Take second derivative. You don't have to find where f'' DNE because it's not important to find the behavior of f' graph. However, f''=0 gives you #'s to compare sign changes. Signs in f'' give you concavity and inflection points of f function. So if ---- 2 ++++ means f is concaving DOWN until 2 and concaving UP after 2. 2 is the inflection point.
Mind you, the 7 and 2 were numbers along the x-axis (after putting f' or f'' equal 0). To find the actual height, or the y value to complete a coordinate, you'd need to plug 7 and 2 in the f function.
8) Graph the function based on the seven guidelines above.