Logarithmic functions
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The document summarizes the key properties of logarithmic functions in 3 sentences: Logarithmic functions have a vertical asymptote at x=0 when b>1 and are undefined for negative values of x, they are symmetric about the y-axis and decrease without bound as x approaches 0 from the right or increases without bound as x approaches 0 from the left when 0<b<1. The graph can be shifted horizontally by changing the argument of the logarithm from x to x+c or x-c, and vertically by multiplying the entire function by a constant.
Logarithmic functions
- 2. Graph of y = log x b >1 b 2 1 1/b 1 b b2 -1 If x = ------ , then y = ------ 1/b -1 1 0 b 1 b2 2
- 3. Sketch the graph of y = log |x| b >1 b y = log (-x) if x < 0 y = log x if x > 0 b b 2 1 -b2 -b -1 1 b b2 If x = ------ , then y = ------ If x = ------ , then y = ------ -1 0 1 0 -b 1 b 1 -b2 2 b2 2 Graph of y = log |x| b>1 b is symmetric with respect to y-axis, that is, logb|x| is an even function.
- 4. Graph of y = log x b<1 b If x = ------ , then y = ------ b 1 1 0 1/b -1 1 1/b2 -2 1 1/b 1/b2 b -1 -2
- 5. Sketch the graph of y = log |x| b<1 b y = log (-x) if x < 0 y = log x if x > 0 b b If x = ------ , then y = ------ If x = ------ , then y = ------ -1 0 1 0 -1/b -1 1/b -1 -1/b2 -2 1/b2 -2 -1/b2 -1/b -1 1 1/b 1/b2 -1 -2 Graph of y = log |x| b<1 b is symmetric with respect to y-axis, that is, logb|x| is an even function.
- 6. Graph of y = log (x+3) 5 1 -3 -2 2 If x = ------ , then y = ------ -2 0 2 1
- 7. Graph of y = log (x-3) 0.5 If x = ------ , then y = ------ 4 0 3.5 1 1 3.5 3 4
- 8. Graph of y = -log (x+3) 0.5 1 -3 -2 -1 If x = ------ , then y = ------ -2 0 -1 1