Question

Use the steps below to sketch the graph y = x^2 - 7x - 18. Required points are the x intercepts and the max and mix of the graph

1. Determine the domain of f.
2. Find the x- and y-intercepts of f.†
3. Determine the behavior of f for large absolute values of x.
4. Find all horizontal and vertical asymptotes of the graph of f.
5. Determine the intervals where f is increasing and where f is decreasing.
6. Find the relative extrema of f.
7. Determine the concavity of the graph of f.
8. Find the inflection points of f.
9. Plot a few additional points to help further identify the shape of the graph of f and sketch the graph.
10. Use the curve-sketching guide above to sketch the graph of the function.

Answer 1

Sol. Ginen function y = f(x) = x²-11-18 0 fear polynomial on n. so fon defined for all real a Domain of of i i (-0,0) put y=0 =) 270-48=0 hant2n-18=0 9 (2–97+212-9)=0 (x+2) (7-9)=0 9 =-2, 1=9 ... a-intercepts (-2,0), (9,0) put 1=0, 4 =0-0-18 =-18 ya intercept ů (0,-18) 1-), f(n)- 00 *mas, f(w) x degree and leading coeffient in positie) asympobles to fon). 3 As enen no 5 -) 21-740 fam) a @ There are f'cm) = 24-7 f'caso f'cuko asz f(a) increases an (1,6), decreases on decreasen an ( -1) 6CM =0 2=1 f(n=230 fcus has minimum value at = £ =) 22-7>0 as1 21-70

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