Graphs of exponential functions and logarithmic functions provide a visual insight into their properties, such as growth, decay, and the inverse relationship between them. Graphs of exponential ...

Any function and its inverse are symmetrical about the line\(y = x\).

Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization ...

where a ¹ 0 and b is a constant called the base of the exponential function. b > 0 and b ¹ 1 x is the independent variable. It is the exponent of the constant, b. Thus exponential functions have a ...

Given \(f(x) = 3x + 2\), we are often asked to find \(f(2)\) or \(f( - 3)\). To do this we substitute \(2\) or \(- 3\) for \(x\). So, \(f(2) = 3(2) + 2 = 8\) and \(f ...

Abstract: We present new exponential bounds for the Gaussian Q function (one- and two-dimensional) and its inverse, and for M-ary phase-shift-keying (MPSK), M-ary ...

Exponential and logarithmic functions are mathematical concepts with wide-ranging applications. Exponential functions are commonly used to model phenomena such as population growth, the spread of ...