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Understanding Logarithmic Functions: Graphs and Symmetry

Learn to sketch graphs of logarithmic functions with varying bases and understand the symmetry properties. Explore transformations and key properties of logarithmic graphs.

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Understanding Logarithmic Functions: Graphs and Symmetry

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  1. Graph of Logarithmic functions

  2. Graph ofy = logbx b >1 2 1 1/b b 1 b2 If x= ------ , then y= ------ 1/b -1 1 0 b 1 b2 2 -1

  3. Sketch the graph ofy = logb|x| b >1 y = logbx if x > 0 y = log b(-x) if x < 0 2 1 b -b -1 1 b2 -b2 If x = ------ , then y = ------ -1 0 -b 1 -b2 2 If x = ------ , then y = ------ 1 0 b 1 b2 2 Graph ofy = logb|x| b > 1 is symmetric with respect to y-axis, that is, logb|x| is an even function.

  4. Graph ofy = logbx b < 1 If x= ------ , then y= ------ b 1 1 0 1/b -1 1/b2 -2 1 1/b2 1 1/b b -1 -2

  5. Sketch the graph ofy = logb|x| b < 1 y = logbx if x > 0 y = log b(-x) if x < 0 If x= ------ , then y= ------ -1 0 -1/b -1 -1/b2 -2 If x= ------ , then y = ------ 1 0 1/b -1 1/b2 -2 1 -1/b2 1/b2 1/b -1 -1/b -1 -2 Graph ofy = logb|x| b < 1 is symmetric with respect to y-axis, that is, logb|x| is an even function.

  6. Graph ofy = log5 (x+3) 1 2 -3 -2 If x= ------ , then y= ------ -2 0 2 1

  7. Graph ofy = log0.5 (x-3) If x= ------ , then y= ------ 4 0 3.5 1 1 3.5 3 4

  8. Graph ofy = -log0.5 (x+3) 1 -1 -3 -2 If x= ------ , then y= ------ -2 0 -1 1

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