Question

A Guide to Curve Sketching 1. Determine the domain of f. 2. Find the x- and y-intercepts off.* 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 fand sketch the graph. DO NOT sketch the graph of f(x) x6x?+ 9x + 2, but use the steps provided and answer any of the steps. Ensure you list the step selected with your answer.

Answer 1

Ans F(x)= x²- 6²+3x+2 Sinca f(x) in a polynomial and is defined Everywhere therefore, 1. Domain of Flat) la: MER lie x6(-00,00) do For tinding x Intercont put y=0 f tas tinding y-intercept put X=0 Y = 4²-62²+9x+2 Put x=0 y=2] → Y-intercept 7 Put y=0 713-6342+3x+2=0 on tinding the roots , it will give only one real root of two imaginery Tools, ide the real oool is 24-019582 (8) For point of intlection tind F"(L) and Equate it to zero . f(x)= 3x²_12x+g F" (%) = 621-12 F"(x)=0 7 62-12=0 H=2 point of Innection (2,4)

6,7)for increasing & decreasing Hind pts. where f'(x)=0 and then check the behaureur of foo & ter concavity Check the behaviour of F"(x). f'()=0 3242_12x+9=0 hal, u=3 F"(x) at x1=1, 6600 - 12=-620 = concave down f"(21) at 2=3 613) -12= 6 >0 (encave up. F() decvaring too ael1,3) f increasing tor 861-00, 1) U(3,0)