Graphical Similarities

The graphs of exponential equations have some similarities. All of the curves graphed in this book pass the vertical line test. They also pass the horizontal line test. Therefore, the exponential curve and the inverse curve are both functions. There was never a restriction on what values could be used for x, so the domain of exponential functions is all real numbers. The range will depend on the value of a. When a is positive, then the range is all positive real numbers. When a is negative, the range is all negative real numbers. Domain and range will be presented in further detail in this unit. All exponential curves have an asymptote. The asymptote will change depending on the values within the equation and will be explored further a little later.

There are some other situations left unexplored, such as the case of y = ab(x-h) + k . The curve will be shifted according to the values of h and k. This situation will be presented later in this unit.


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