Exponential functions are functions in the form of f(x) = a^x, where a is a constant and x is the variable. Logarithmic functions are the inverse of exponential functions and are in the form of f(x) = loga(x), where a is the base.
The main difference between exponential and logarithmic functions is that exponential functions increase rapidly as the input increases, while logarithmic functions increase slowly. Additionally, exponential functions have a horizontal asymptote at y=0, while logarithmic functions have a vertical asymptote at x=0.
Exponential functions are commonly used to model population growth, compound interest, and radioactive decay. They are also used in fields such as physics, biology, and economics.
To graph an exponential function, plot points by choosing different values of x and calculating f(x). Then, connect the points with a smooth curve. To graph a logarithmic function, plot points by choosing different values of x and calculating f(x). Then, connect the points with a smooth curve and make sure to include the vertical asymptote at x=0.
The relationship between exponential and logarithmic functions is that they are inverse functions of each other. This means that if you plug the output of one function into the other, you will get the original input. For example, if you plug an x-value into an exponential function and then take that output and plug it into the inverse logarithmic function, you will get the original x-value.