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What happens to the graph of an exponential function if b is a function between 0 and 1?
This question appears to relate to some problem for which we have no information. The graph of an exponential function shows a doubling at regular intervals. But we are not told what the role is of b, so we cannot comment further.
Graph Inverse function of the exponential function?
An exponential function is of the form y = a^x, where a is a constant. The inverse of this is x = a^y --> y = ln(x)/ln(a), where ln() means the natural log.
What are some characteristics of the graph of an exponential function?
An exponential function is a nonlinear function in the form y=ab^x, where a isn't equal to zero. In a table, consecutive output values have a common ratio. a is the y-intercept of the exponential function and b is the rate of growth/decay.
A logarithmic function takes the exponential function's and returns the exponential function's input?
output
What determines whether the on a graph of an exponential functions increases or decreases?
An exponential function such as y=b^x increases as x goes to infinity for all values in the domain. That is, the function increases from left to right anywhere you look on the graph, as long as the base b is greater than 1. This is called a "Growth" function. However, the graph is decreasing as x goes to infinity if (a) the opposite value of the input is programmed into the function, as in y=b^-x, or if (b) the base is less than 1, as in y=(1/2)^x.
