I have attached a graphing assingment for my calculus class. Please follow the instructions and do as it says.
zeig013
mac_2233_graphing_assignment.pdf
MAC 2233 Graphing Assignment
A General Procedure for Sketching the Graph of f(x)
Step 1. Find the domain of f(x) [that is where f(x) is defined].
Step 2. Find and plot all intercepts. The y-‐intercept (where x = 0) is usually easy to find, but the x-‐intercepts [where f(x) = 0] may require a calculator.
Step 3. Determine all vertical and horizontal asymptotes of the graph. Draw the asymptotes in a coordinate plane.
Step 4. Find f’(x), and use it to determine the critical numbers of f(x) and intervals of increase and decrease.
Step 5. Determine all relative extrema (both coordinates). Plot each relative maximum with a cap (∩) and each relative minimum with a cup (∪).
Step 6. Find f’’(x), and use it to determine intervals of concavity and points of inflection. Plot each inflection point with a “twist” to suggest the shape of the graph near the point.
Step 7. You now have a preliminary graph, with asymptotes in place, intercepts plotted, arrows indicating the direction of the graph, and caps, cups, and twists suggesting the shape at key points. Plot additional points if needed, and complete the sketch by joining the plotted points in the directions indicated. Be sure to remember that the graph cannot cross a vertical asymptote.
Follow the seven steps and graph: (5 points each)
1. 𝑓 𝑥 = 𝑥( − 4𝑥+
2. 𝑓 𝑥 = 𝑥+ − 3𝑥 + 1 (the x-‐intercepts are: -‐1.88, 0.35, 1.53)
3. 𝑓 𝑥 = / /01
4. 𝑓 𝑥 = 1/ 2
/20 3 (𝑓55 / = 31/
26 ( /203 7
)
5. 𝑓 𝑥 = (𝑥 + 1) 2 7
