Exponential Function Exponential Function In mathematics, the exponential function is the function ex, where e is the number (approximately 2.718281828) such that the function ex is its own derivative.[1][2] The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e. percentage increase or decrease) in the dependent variable. The function is often written as exp(x), especially when it is impractical to write the independent variable as a superscript. The graph of y = ex is upward-sloping, and increases faster as x increases. The graph always lies above the x-axis but can get arbitrarily close to it for negative x; thus, the x-axis is a horizontal asymptote. The slope of the tangent to the graph at each point is equal to its y coordinate at that point. The inverse function is the natural logarithm ln(x); because of this, some old texts refer to the exponential function as the antilogarithm. Sometimes the term exponential function is used more generally for functions of the form cbx, where the base b is any positive real number, not necessarily e.
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See exponential growth for this usage. In general, the variable x can be any real or complex number, or even an entirely different kind of mathematical object; see the formal definition below Many students don't like subjects in which they have to learn large answers, dates and, etc. but they, enjoy solving math questions, because it seems simple to them. Are you thinking that I like learning different things but, when it comes to solve math question I always move away. Dear friends, math is really very simple subject, some students feels it boring because they don't understand the concept behind the problem. In this article, I will give you a brief idea of exponential functions and x -- y intercept. exponential functions is the function ex, where e is the number such that the function ex is its own derivative. The value of ex is approximately 2.718281828, and daily there is an increase in the value of exponential function as many math scientists do new research. The graph of y = ex is upward sloping, and increases rapidly when x increases, that means they both are directly proportional to each other. The graph lies above the x-axis but can get arbitrarily close to its negative axis. Due to this x is called as horizontal asymptote. At each point, the slope of the tangent to the graph is equal to its y coordinate at that point. The natural logarithm is the inverse of exponential function. After talking about exponential, one of the difficult topic now, move to a simple topic that is x -- intercept and y -- intercept. It is simple to understand this concept. When a graph crosses the x- axis it is called as x- intercepts and y -intercept is where the graph crosses the y- axis.
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The main problem in this topic arises when we have to deal with intercepts algebraically. To understand this part, just think about axes. In Cartesian plane, you were shown the regular number line from elementary school x- axis and a line perpendicular to number line through zero is called y- axis. So, in algebraic terms, an x- intercept is a point on the graph where y is equal to zero, and a y- intercepts is a point where x is equal to zero. If we specify it more, then an x intercept is a point where the value of y is zero and vice- versa for y intercept. To learn more about these topics start taking benefit of online help, and solver where you will get all latest updates and concepts of mathematics.
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