Putting it all together! In this video, we tackle the ultimate Calculus I challenge: Curve Sketching. We take a complex function and analyse every single part of it to draw a perfect graph without using a calculator. In this complete walkthrough, we will cover: Step 1: Domain: Check the domain of the function Step 2: Positivity: Find where the function is positive or negative Step 3: Limit at the extreme of the domain: horizontal and vertical asymptote Step 4: Local Extrema: Using the Quotient Rule to find critical points and intervals of increase/decrease. Step 5: The Sketch: Bringing all the clues together to draw the final graph. This video is the "Capstone" of our Calculus I module. It combines limits, differentiation rules, and the max/min tests into one big problem. Need a refresher on the steps? Watch the Limits & Asymptotes video here: Watch Max/Min Theory here: Watch Max/Min Exercise here: If you are preparing for your final calculus exam, this is the perfect review. Leave a like if it helps! Grab your pen and paper—this is a big one!