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Key Exploring the Graphs of Logarithmic Functions 1) ! y = log 3 x x 1/9 1/3 1 3 9 2) y !x = 3 2 y = x, x = 2 y x 1/4 1/2 1 2 4 Key y -2 -1 0 1 2 y -2 -1 0 1 2 Page 1 of 6 ©Let’s Algebra 2014 3) 7 = x, x = 7 y y x 1/7 y -1 1 0 7 1 4) This part was done for student. 5) ! y = log 5 x The x- intercept = 1 and the point (5, 1) is on the line. Key 6) The domain is x > 0. The range is all real numbers. 7) The x-intercept is (1, 0). There is no y-intercept. 8) The asymptote is x = 0. Page 2 of 6 ©Let’s Algebra 2014 y = log 5 x 9) y = log 5 (x ! 3) + 2 The x-intercept = 1 The point ( 5 , 1 ) is on the line. (8, 3) (4, 2) The domain of the “new” function is x>3 The range of the “new” function is all real numbers. The asymptote of the “new function is x = 3 Exercises a) ! y = log 8 x The x- intercept = 1 and the point (8, 1) is on the line. The domain is x > 0. The range is all real numbers. The x-intercept is (1, 0) The y-intercept is…there is no y-intercept. The asymptote is x = 0. Key Page 3 of 6 ©Let’s Algebra 2014 b) ! y = log 4 x The x- intercept = 1 and the point (4, 1) is on the line. The domain is x > 0. The range is all real numbers. The x-intercept is (1,0) The y-intercept is …there is no y-intercept. The asymptote is x = 0. c) ! y = log x The x- intercept = 1 and the point (10, 1) is on the line. The domain is x > 0. The range is is all real numbers. The x-intercept is (1,0) The y-intercept is…there is no y-intercept The asymptote is x = 0. Key Page 4 of 6 ©Let’s Algebra 2014 y = log 6 x d) y = log 6 (x ! 2) ! 3 The x-intercept is 1. The point (6, 1) is on the graph. The domain of the “new” function is x > 2. The range of the “new” function is all real numbers. (3, –3) (8, –2) y = log 8 x e) The asymptote of the “new” function is x = 2. y = ! log 8 (x + 4) ! 1 The x-intercept is 1. The point (8, 1) is on the graph. The domain of the “new” function is x > -4 The range of the “new” function is all real numbers. The asymptote of the “new” function is x = -4. (–3, –1) Key (4, –2) Page 5 of 6 ©Let’s Algebra 2014 Without graphing, describe the transformation from the parent function. f) It is translated right 1 unit. g) It is translated down 1 unit. h) It is translated right 2 units and down 5 units. i) It it vertically compressed by a factor of .5 and reflected across the x-axis, then translated right 1 unit, and up 2 units. j) It is vertically stretched by a factor of 2 and reflected across the x-axis, then translated left 5 units, up 3 units. Key Page 6 of 6 ©Let’s Algebra 2014