Checkpoint: Assess Your Understanding, pages

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1 Checkpoint: Assess Your Understanding, pages Multiple Choice Given the graph of the function f(), which graph below right represents = f()? f() D C A B Chapter : Radical and Rational Functions Checkpoint Solutions 17

2 . For each function f()graphed below: Sketch the graph of = f(). State the domain and range of = f(). Eplain wh the domains are different and the ranges are different. a) b) 6 f() f() f() 6 f() Mark points where or 1. The graph of f() is above the graph of f() between these points. Choose, then mark other points on the graph of f(). f() 3 f() 1. f() is not defined for < < 6. Mark points where or 1. Choose, then mark other points on the graph of f(). f() 5 f() Join the points with a smooth Join the points with smooth curve. curves. Domain is:» 6 Domain is: or» 6 Range is:» Range is:» The domain of a linear function or a quadratic function is all real values of, but the square root of a negative number is undefined, so an value of that makes the radicand negative is not in the domain of a radical function. The range of the linear function is all real values of, and the range of the quadratic function is all real values of that are greater than or equal to. The principal square root of a number is alwas or positive, so the range of the radical functions is restricted to these values of. 18 Chapter : Radical and Rational Functions Checkpoint Solutions DO NOT COPY. P

3 3. Solve each radical equation b graphing. Give the solution to the nearest tenth. a) = - 1 b) + = Write the equation as: 3 1 Graph the related function: f() 3 1 Use graphing technolog to determine the approimate zero: So, the solution is: 1.6 Write the equation as: 5 3 Graph the related function: f() 5 3 Use graphing technolog to determine the approimate zero: So, the solution is: Use graphing technolog to graph each rational function. Identif an non-permissible values of and the equations of an horizontal asmptotes. 3 a) = 3 b) = + - Since, then The vertical asmptote has equation. The horizontal asmptote has equation 3. Since, then The vertical asmptotes have equations and. The horizontal asmptote has equation. c) d) = - = Since 3, then The vertical asmptote has equation. There is no horizontal asmptote. Since 3, then There is a hole at. There is no horizontal asmptote Multiple Choice Which function has a graph with a hole? A. = + B. = C. = + D. = Chapter : Radical and Rational Functions Checkpoint Solutions 19

4 6. Match each function to its graph. Justif our choice. i) Graph A ii) Graph B f() g() 6 iii) Graph C iv) Graph D k () h() 1 a) b) = = There is a vertical asmptote with equation 3. The degrees of the numerator and denominator are equal, so there is a horizontal asmptote that is not the -ais. The function matches Graph B. ( 5)( 3) Factor:, 3 ( 5)( 3) or 3 There is a hole at 3. The function matches Graph C. c) = - 3 d) = - 3 There is a vertical asmptote with equation 3. The degree of the numerator is 1 more than the degree of the denominator, so there is an oblique asmptote. The function matches Graph D. The function is not defined for 3 ; that is, 3. So, there are vertical asmptotes at and 3 3. The degrees of the numerator and denominator are equal, so there is a horizontal asmptote that is not the -ais. The function matches Graph A. Chapter : Radical and Rational Functions Checkpoint Solutions DO NOT COPY. P

5 7. For the graph of each rational function below, determine without technolog: i) the equations of an asmptotes and the coordinates of an hole ii) the domain of the function Use graphing technolog to verif the characteristics. a) = 5 - i) The function is undefined when 5 ; that is, when 5. There are no common factors, so there are vertical asmptotes with equations 5 and 5. The degrees of the numerator and denominator are equal, so there is a horizontal asmptote. The leading coefficients of the numerator and denominator are and 1, respectivel. So, the horizontal asmptote has equation: ii) The domain is: 5 b) = i) The function is undefined when 3 ; that is, when 3. ( 3) Factor: 3 There is a hole at 3. The function is:, 3 The coordinates of the hole are: ( 3, 6) ii) The domain is: 3 8. Solve each rational equation b graphing. Give the solution to the nearest tenth. a) b) = = -5 Graph a related function: 3 5 f() 3 Use graphing technolog to determine the zeros: 1.8 or 6. Graph a related function: f() Use graphing technolog to determine the zeros: 9.1 or 1.1 Chapter : Radical and Rational Functions Checkpoint Solutions 1