For Question 5 use the following rational function to answer

For Question 5, use the following rational function to answer the questions. f(x)--4x+3 x2 +2x-3 a. Find the domain. b. Find the vertical asymptote(s), if any. c. Are there any holes in the graph? If yes, find the coordinates of the hole. d. Find the horizontal or oblique asymptotes, if any e. Does the graph cross the horizontal or oblique asymptotes? If yes, where does it cross? f. Graph this function. Indicate all intercept(s) and asymptotes y. 6 5 3 2 2 3 4 5 6 x -6-5-4-3-2-1 O1 3 5

Solution

f(x)= (x²-4x+3)/(x²+2x-3) =(x-3)(x-1)/(x+3)(x-1) = (x-3)/(x+3)

Hole is at x-1=0

x=1

Vertical asymptote , x+3=0

x=-3

Horizontal asymptote

Numerator\'s and denominator\'s degree are equal

Therefore HA, y=1

Domain

Denominator should not be 0

Thereore domain (-infinity,-3)U(-3, infinity)