Complete the table below for 2nd function assigned fx x 2x

Complete the table below for 2^nd function assigned: f(x) = x - 2/x^2 - 4x + 3 Is the graph a rational function or polynomial? From your knowledge of common function shapes, what shape can you prediction? Find the x & y intercepts Does the function have any vertical asymptotes? Yes/No If yes, how many? Using the correct notation, name them Does the function have a horizontal asymptote? Yes/No Using the correct notation, name the horizontal asymptote Generate the first derivative Name the 1^st derivative, using the correct notation What are all possible critical numbers? Generate a real number line, indicate where the function is increasing & decreasing, and record the minimums & maximums Find the 2^nd derivative Name the second derivative What are the x-values of possible critical numbers from the 2^nd derivative? Using the correct notation, generate a real number line and indicate concavity. Name any inflection point. Take the limit of the function as X rightarrow infinity; what does this indicate? Take the limit of the function as X rightarrow -infinity; what does this indicate? Complete the process by graphing the function on graph paper

Solution

11. Since the graph can be expressed in the form p/q, it\'s a rational function.

12. The prediction is of the shape of reciprocal function.

13. In rational function, we set numerator=0 to find x intercept.

So, x-2=0

So, x=2. So, (2,0) is the x intercept.

To find y intercept, we have to plug x=0 into the rational function. When we plug x=0, we woud get -2/3

So, y intefcept is (0 , -2/3)

14. Vertical Asymptotes are found by setting denominator = 0.

a) Yes, the function has vertical asymptotes.

b) Since degree of denominator is 2, it has two vertical asymptotes.

c) x²-4x+3=0

(x-3)(x-1)=0

x-3=0 and x-1=0

So, x=3 and x=1 are the vertical asymptotes.