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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.

Q: What happens to the graph of an exponential function if b is a function between 0 and 1?

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f(x)=2X-2

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.

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.

As time passes - as the graph goes more and more to the right, usually - the graph will get closer and closer to the horizontal axis.

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.

Related questions

The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.

f(x)=2X-2

Yuo cannot include a graphical illustration here. Take a look at the Wikipedia, under "exponential function" and "logistic function". Basically, the exponential function increases faster and faster over time. The logistics function initially increases similarly to an exponential function, but then eventually flattens out, tending toward a horizontal asymptote.

The graph of an exponential function f(x) = bx approaches, but does not cross the x-axis. The x-axis is a horizontal asymptote.

an exponential function flipped over the line y=x

It is an 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.

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.

base

As time passes - as the graph goes more and more to the right, usually - the graph will get closer and closer to the horizontal axis.

If you want to find the initial value of an exponential, which point would you find on the graph?

No, it would not.