PRE CALCULUS 12 TRANSFORMATIONS, RADICAL AND RATIONAL FUNCTIONS. 1. Sketch the graph of y 3 x 2 15 x 18 x2 x 6 and show all asymptotes with a dotted line. i) Equation of any vertical asymptote(s) __________________________________________ ii) State any restrictions or non-permissible value(s) ___________________________________________ iii) Determine coordinates of any intercept(s). (algebraically) 3 marks __________________________________________ iv) Describe the behavior of the function as it approaches and leaves vertical asymptotes and/or point of discontinuity. _________________________________________________________________________________________ _________________________________________________________________________________________ v) State the horizontal asymptote. _________________________________________________________________________________________ vi) State the Domain and Range __________________________________________________________________ __________________________________________________________________ 2. For the function y f x defined by the diagram below, sketch each graph on the grid provided. For each graph, explain what change you made to y f x . Also, give the new coordinates of the point mentioned in each question. 5 5 5 5 a) y 2 f x 5 _______________________________________ 5 5 _______________________________________ 5 b) 5 4, 1 ____________ 2 y f x _______________________________________ 5 5 _______________________________________ 5 2, 2 ___________ c) x f y 5 _______________________________________ 5 5 5 _______________________________________ 7, 2 d) 5 ___________ y f 2x 4 3 _______________________________________ 5 5 5 3. Write the equation of the transformed function y _______________________________________ 4, 1 ____________ x after the following transformations. a) A reflection in the x-axis followed by a translation of 4 units left. a)__________________________ b) A horizontal expansion by a factor of 4 followed by a translation of 3 units right and then 7 units down. b)________________________ 4. 3x Given the function f x x 7 , determine the equation of the inverse function, f 5. 1 Given the graph of the function y f x below, sketch the graph of y 2 f 2 x 1on the grid provided. 1 x . 5 5 5 5 5 5 5 5 5.)_____________________________ PRE CALCULUS 12 TRANSFORMATIONS, RADICAL AND RATIONAL FUNCTIONS. 1. Sketch the graph of y 3 x 2 15 x 18 x2 x 6 and show all asymptotes with a dotted line. i) Equation of any vertical asymptote(s) __________________________________________ ii) State any restrictions or non-permissible value(s) ___________________________________________ iii) Determine coordinates of any intercept(s). (algebraically) 3 marks __________________________________________ iv) Describe the behavior of the function as it approaches and leaves vertical asymptotes and/or point of discontinuity. _________________________________________________________________________________________ _________________________________________________________________________________________ v) State the horizontal asymptote. _________________________________________________________________________________________ vi) State the Domain and Range __________________________________________________________________ __________________________________________________________________ 2. For the function y f x defined by the diagram below, sketch each graph on the grid provided. For each graph, explain what change you made to y f x . Also, give the new coordinates of the point mentioned in each question. 5 5 5 5 a) y 2 f x 5 _______________________________________ 5 5 _______________________________________ 5 b) 5 4, 1 ____________ 2 y f x _______________________________________ 5 5 _______________________________________ 5 2, 2 ___________ c) x f y 5 _______________________________________ 5 5 5 _______________________________________ 7, 2 d) 5 ___________ y f 2x 4 3 _______________________________________ 5 5 5 3. Write the equation of the transformed function y _______________________________________ 4, 1 ____________ x after the following transformations. a) A reflection in the x-axis followed by a translation of 4 units left. a)__________________________ b) A horizontal expansion by a factor of 4 followed by a translation of 3 units right and then 7 units down. b)________________________ 4. 3x Given the function f x x 7 , determine the equation of the inverse function, f 5. 1 Given the graph of the function y f x below, sketch the graph of y 2 f 2 x 1on the grid provided. 1 x . 5 5 5 5 5 5 5 5 5.)_____________________________