Worksheet A: (Topics 1.9 - 1.10) Vertical Asymptotes and Holes Name: or vertical asymptote. Directions: For each of the following rational functions, determine and label any values of x where the graph has a hole 1. f (x) = (x-1)(x-5) 2. 8 (x)= (x+3) (x-1) (x -5) (x+2) (x-3)(x+1) 3. h (x ) = ( *+ 4) (x-6) hole = * - 3 (x-6)(x-6) hole * * = 2 JA = X = 5 VAX = - 1 4. k ( x ) = ( x -8) ( x + 2)2 5 . r ( x ) = * + x - 6 x(x- 1) (x+2) x 3 - 4x 6. p(x) = x-1 x 2 + 1 Directions: For each of the following, write the left and right limit statements for f (x) as x approaches 3. 7. f (x ) = (x+2) (x-6) 8 . f ( x ) = - (x-3) (x+3) x(x- 3) 9 . f ( x ) = -2 x - 3 ( * - 3 ) Left: Left: Left: Right: Right: Right: Directions: Write an equation of a rational function that has the following properties. 10. The graph of f has a hole at x = 3 and vertical asymptotes at x = 1 and x = -4. 1 1. The graph of g has a hole at x = -1, a vertical asymptote at x = 7, and a zero at x = -2. 12. The graph of h has a hole at x = 2 and x = 5, a vertical asymptote at x = 0, and a zero at x = 1