K – equal to the value of the horizontal asymptote
#EXPONENTIAL GRAPH HOW TO#
Below is a list of all of the variables we may have to look for, and how to usually find them:Ī – solve for it using algebra, or it will be givenī – solve for it using algebra, or it will be givenĬ – let x = 0 and imagine "c" is not there, the value of y will equal the y-intercept now count how many units the y value for the y-intercept is from the y-axis, and this will equal "c" Given the graph of exponential functions, we need to be able to take some information from the graph itself, and then solve for the stuff we are unable to take directly from the graph. Given an exponential function graph, how can we find the exponential equation? How To Find Exponential Functionsįinding the equation of exponential functions is often a multi-step process, and every problem is different based upon the information and type of graph we are given. Take your time to play around with the variables, and get a better feel for how changing each of the variables effects the nature of the function. To get a better look at exponential functions, and to become familiar with the above general equation, visit this excellent graphing calculator website here. There is no value for x we can use to make y=2.Īnd that's all of the variables! Again, several of these are more complicated than others, so it will take time to get used to working with them all and becoming comfortable finding them. For our other function y = 2 x + 2 y=2^x+2 y = 2 x + 2, k=2, and therefore the horizontal asymptote equals 2. This makes sense, because no matter what value we put in for x, we will never get y to equal 0.
Take for example the function y = 2 x y=2^x y = 2 x: for this exponential function, k=0, and therefore the "horizontal asymptote" equals 0. "k" is a particularly important variable, as it is also equal to what we call the horizontal asymptote! An asymptote is a value for either x or y that a function approaches, but never actually equals. If "k" were negative in this example, the exponential function would have been translated down two units. Let's compare the graph of y = 2 x y=2^x y = 2 x to another exponential equation where we modify "a", giving us y = ( − 4 ) 2 x y=(-4)2^x y = ( − 4 ) 2 xīy making this transformation, we have translated the original graph of y = 2 x y=2^x y = 2 x up two units. But, so you have access to all of the information you need about exponential functions and how to graph exponential functions, let's outline what changing each of these variables does to the graph of an exponential equation. In this lesson, we'll only be going over very basic exponential functions, so you don't need to worry about some of the above variables. The above formula is a little more complicated than previous functions you've likely worked with, so let's define all of the variables.Ī – the vertical stretch or compression factorĭ – the horizontal stretch or compression factor Y = a b d ( x − c ) + k y=ab^+k y = a b d ( x − c ) + k Now that we have an idea of what exponential equations look like in a graph, let's give the general formula for exponential functions: That is because as x increases, the value of y increases to a bigger and bigger value each time, or what we call "exponentially". In the case of y = 2 x y=2^x y = 2 x and y = 3 x y=3^x y = 3 x (not pictured), on the other hand, we see an increasingly steepening curve for our graph.
That is why the above graph of y = 1 x y=1^x y = 1 x is just a straight line. As you can see, for exponential functions with a "base value" of 1, the value of y stays constant at 1, because 1 to the power of anything is just 1. The table of values of y = 1^x and y = 2^xĪbove you can see three tables for three different "base values" – 1, 2 and 3 – all of which are to the power of x.
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