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 Dependent Variable

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# Graphing Logarithmic Functions

Example

Graphs A, B, C, and D represent functions of the form y = bx and y = logbx, where b is the base of each function. Here, b > 0 and b 1.

a. Which graph represents an exponential function where b > 1?

b. Which graph represents an exponential function where 0 < b < 1?

c. Which graph represents a logarithmic function where b > 1?

d. Which graph represents a logarithmic function where 0 < b < 1?

Solution

a. Graph C. Because b > 0, the y-values of an exponential function will all be positive. Also, because b > 1, as the x-values increase, the y-values will increase. (The function for graph C is y = 2x.)

b. Graph B. Because b > 0, the y-values of an exponential function will all be positive. Because 0 < b < 1, as the x-values increase, the y-values will decrease. (The function for graph B is )

c. Graph A. The inverse of a logarithmic function where b > 1 is an exponential function where b > 1. If the graph of an exponential function where b > 1 (such as graph C) is reflected across the line y = x, we obtain a graph like graph A. (The function for graph A is y = log2x.)

d. Graph D. The inverse of a logarithmic function where 0 < b < 1 is an exponential function where 0 < b < 1. If the graph of an exponential function where 0 < b < 1 (such as graph B) is reflected across the line y = x, we obtain a graph like graph D. (The function for graph D is y = log 1/2 x.)