RADICAL AND RATIONAL FUNCTIONS REVIEW

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1 RADICAL AND RATIONAL FUNCTIONS REVIEW Name: Block: Date: Total = % Page of 4 Unit 2

2 . Sketch the graph of the following functions. State the domain and range. y = 2 x + 3 Domain: Range: 2. Identify the transformations for each of the following from y = x ( ) a. y = 9 x 3 b. y = 4x+ 8 c. y+ 3= x 3 ( ) 202 Page 2 of 4 Unit 2

3 3. Write the equation of the radical function that results from the following transformations on the graph of y = x in the order presented. a. Horizontal expansion by a factor of 5 and a vertical translation down 3 units. a. b. Vertical compression by a factor of one third, reflection in the y axis, horizontal translation 4 units left. b. c. Vertical expansion by a factor of four, reflection in the x axis, horizontal compression by a factor of one-sixth and a translation 5 units left and unit up. c. 4. Write the equation of each of the following. Use the form = ( ) a. b. y a b x h + k Equation: Equation: 202 Page 3 of 4 Unit 2

4 c. Equation: 5. Given the graph of y= f( x) graph the function that would represent y= f( x) List the domain and range of each graph, list the EXACT VALUES of any invariant points. y= f( x) y= f( x) Domain f ( x ) : Domain f ( x ) : Range f ( x ) : Range f ( x ) : 5. Invariant Points: 202 Page 4 of 4 Unit 2

5 6. Given the graph of y = f( x) on the left, and f ( x) = ( x 2) 2 7 graph the function that would represent y= f( x). List the domain and range of each graph, list the EXACT VALUES of any invariant points. y= f( x) y= f( x) Domain f ( x ) : Domain f ( x ) : Range f ( x ) : Range f ( x ) : 6. Invariant Points: 7. Compare the domains and ranges of the following two functions. Using graphing calculator. ( each) a. f ( x) = 8 2 x and f ( x) = 8 2x 2 2 Domain f ( x): Domain f ( x): Range f ( x): Range f ( x): 202 Page 5 of 4 Unit 2

6 8. Solve each of the following algebraically for their exact values. a. 3x 5 = 3 b. x + 5 3= 3 a. b. c. 2 3x 2 = x c. 202 Page 6 of 4 Unit 2

7 9. ***Bonus: Graphing Calculator question! Solve the following graphically for a decimal approximation to the nearest 00 th. 3x = x Page 7 of 4 Unit 2

8 0. Sketch the graphs of the following functions and show all asymptotes with a dotted line. ( for graph) a 3x 5 x + 4 y =. i) Equation of any vertical asymptote(s) ii) State any restrictions or non-permissible value(s) iii) Determine coordinates of any intercept(s). (algebraically) 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 202 Page 8 of 4 Unit 2

9 b. y = 2x 6 2 x 5x+ 4 i) Equation of any vertical asymptote(s) ii) State any restrictions or non-permissible value(s) iii) Determine coordinates of any intercept(s). (algebraically) 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 202 Page 9 of 4 Unit 2

10 c. y = 2 3x 8x x 2x 8 i) Equation of any vertical asymptote(s) ii) State any restrictions or non-permissible value(s) iii) Determine coordinates of any intercept(s). (algebraically) 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 202 Page 0 of 4 Unit 2

11 . Write a possible equation for each of the following graphs. Explain your reasoning. a. b. a. 2. Write the equation of a possible rational function with the following characteristics. Explain your reasoning. a) Vertical asymptotes at x = ± 3, x intercepts of x = 5 and x =, and a horizontal asymptote of y = 2 b. a. 202 Page of 4 Unit 2

12 b) Vertical asymptotes at x =, x intercept of x = 0, and a discontinuous point at 4 5 5, 9 b. c) Y-intercept at 5, no x-intercepts, discontinuous points at (, 5) and (3, 5) c. 3. Solve each of the following rational functions algebraically for their exact values. 8 a) = 2 ( x ) 2 b) x = x 3x + 8 a. b. 202 Page 2 of 4 Unit 2

13 3x x c) = 4x + 2x c. 2x x x + d) = 2 2 x x 4x + 3 x 3 d. 202 Page 3 of 4 Unit 2

14 4. A river boat can travel at 20 km per hour in still water. The boat travels 30 km upstream against the current then turns around and travels the same distance back with the current. If the total trip took 7.5 hours, what is the speed of the current? Solve this question algebraically as well as graphically. a) Algebra Solution a. b) Bonus: graphing calculator! Graphical. 202 Page 4 of 4 Unit 2

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