If we instead consider logarithmic functions with a base [latex]b[/latex], such that [latex]0 0[/latex], the graph of [latex]y=log{_b}x[/latex] and the graph of [latex]y=log{_\frac{1}{b}}x[/latex] are …

In general, for any base \(b>0\), \(b≠1\), the function \(g(x)=\log_b(x)\) is symmetric about the line \(y=x\) with the function \(f(x)=b^x\). Using this fact and the graphs of the exponential …

Examples demonstrate how to evaluate and use exponential functions in various contexts, such as modeling population growth or radioactive decay. 13.2E: Exercises; 13.3: Graphs of …

Jan 24, 2020 · In this chapter, we will explore exponential functions, which can be used for, among other things, modeling growth patterns such as those found in bacteria. We will also …

The graph of an exponential function is shown in green. The graph shown in light red is the inverse of the exponential function. The line y = x is actually the line of symmetry between the …

Mar 18, 2025 · Analyzing Exponential Graphs. To analyze an exponential graph, it is essential to determine the function’s base, (a), and understand how it influences the shape and behavior of …

Graphing Exponential and Logarithmic Functions Exponential Function – An exponential function is any function that can be written in the form of f(x) = 𝑎 , where x is a real number, a > 0 and a≠ …

We see that the graphs of the exponential and logarithm are symmetric = mirror images. Fact: For > 1, the graph of ( ) = log ( ) has an x-intercept at = 1 and a vertical asymptote at = 0 (the …

Explain the relationship between exponential and logarithmic functions. Describe how to calculate a logarithm to a different base. Identify the hyperbolic functions, their graphs, and basic …

In fact if [latex]b>0[/latex], the graph of [latex]y=log{_b}x[/latex] and the graph of [latex]y=log{_\frac{1}{b}}x[/latex] are symmetric over the [latex]x[/latex]-axis. Thus, if we …