Name: Score /35 Math 30-1 Unit 7: Radical and Rational Functions Assignment Each question is worth 2 marks -- must show work to earn the full mark. Multiple Choice 1. Given the function f(x) : Ixh +k with a domain of {xlx 2 5, x e R} and a range of {yly 2 8, y e R}, which of the following best describes the vertical and horizontal translations with respect to the graph of f(x) = J; ? A 5 units to the left and 8 units up C 8 units to the left and 5 units up B 8 units to the left and 5 units down D 5 units to the left and 8 units down 2. Which is the graph of the square root of the function f(x) = (x 4)2 3? A y C y B: F: r: . For the graph of y =f(x) shown below, which graph best represents y = 4 f(x) ? ID: 4. Which of the reciprocal functions has a vertical asymptote at x = A f(x)=2x1+9 B f
= 5. Which graph represents the function f(x) = A y I 6 1n C f (X) = D f(X) = _4 _ x9 C 5? 9 x+2 1 H2 2 2? 2 ID: ID: A 6. Which graph represents f(x) = x+4 4x2 + 14x-8 - ? A C $ 4 3 2 -1 B D 5 14 3 -2 7. Which rational function has the following characteristics? . a vertical asymptote with equation x = 2 . a horizontal asymptote with equation y = 8 a point of discontinuity at (3, 9) A f (x ) = - x - 3 C f (x) = 7 x +3 (x+ 3) (x - 2) -8 (x + 2) (x+ 3) 7 -+8 B f(x) = x-3 (x -3)(x-2) +8 D f(x) = x - 2 (x - 3) (x+2) + 8 4IDzA 8. Given the function f(x) : / 4, which of the following is a restriction on the inverse function, f1 (x)? A x28 C JCS4 B x24 D x24 Short Answer 9. For the graph of y =f(x) shown below, what are the domain and range of y = 4/ f(x) ? Zk 5x+k 10. What is the value of k in the function f(x) = if its graph passes through the point (3, _ll9) ? 3 11. If (36,6) is a point on the function f(x) = J; , what point must be on the function _5f[_Z (x 6)] + 7 ID:A 12. For the graph of this rational function, state the domain and write the equations of any asymptotes and the coordinates of any hole. y_# ' x23x+2 13. For the graph of y =f(x) shown below, sketch the graph of y = 4/ f(x) . 7 y 3167 0 14. Convert f(x) = x + 9 to the form f(x) = x _ h +k 2x2 2 15. Sketch the graph of y = 2 . x + l y l7 4 7 a3 a2 11 3 x 16. Does the graph of this function have any holes or vertical asymptotes? Write the coordinates of any holes and the equations of any vertical asymptotes. :5x240x+60 y x22x24 ID: IDzA (36-2) 17. Identify the (x,y)coordinate of the point of discontinuity for the function f(x) = 2. x + 3x 10 ax+b cx+d 18. Determine an equation in the form f(x) = y = 130 and a yintercept of 11. for a function that has asymptotes with equations x = 4 and
