Exponential graph is the graph of an exponential function. It always has a horizontal asymptote but no vertical asymptote. Graphing of exponential function can be done by plotting the horizontal asymptote, intercepts, and a few points on it. Show
Let us see how to draw an exponential graph in detail and let us see what the exponential growth graph and exponential decay graph would look like. What is Exponential Graph?An exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid. It always cuts the y-axis at some point but it may or may not cut the x-axis. i.e., an exponential graph always has a y-intercept but it may or may not have the x-intercept. The exponential graph may look in one of the following ways. Graphing Exponential FunctionGraphing exponential function is the process of drawing the curve representing it. An exponential function is of the form f(x) = ax, where 'a' is a constant and a > 0. The value of ax is never 0 for any value of x and so y = 0 is the horizontal asymptote of the exponential function f(x) = ax. The horizontal asymptote plays an important role in the process of the graphing exponential function. The horizontal asymptote of an exponential function is nothing but its vertical shift (i.e., it is a number that is being added to ax). For example, the horizontal asymptote of f(x) = 2x is y = 0 and the horizontal asymptote of g(x) = 2x - 3 is y = -3. Here are the steps to draw the exponential graph in the easiest way.
Here is an example of graphing exponential function. Example: Graph the exponential function f(x) = 2x - 3. Solution: The horizontal asymptote is y = -3. For y-intercept, put x = 0. Then we get y = 20 - 3 = 1 - 3 = -2. So the y-intercept is (0, -2). For x-intercept, put y = 0. Then we get 0 = 2x - 3 ⇒ 2x = 3 ⇒ x = log2 3 ≈ 1.6. So the x-intercept is (1.6, 0). Now, we will create the table of the exponential function.
Let us plot all this information to obtain the exponential graph. Here, the graph has a negative y-intercept and a positive slope (increasing curve). Exponential Growth Graph and Exponential Decay GraphThe above graph is increasing (see from left to right always) and hence that graph represents exponential growth. Note that the function that represents the above graph is f(x) = 2x - 3 where the base is "2" and is "greater than 1". So in general, for any exponential function f(x) = ax,
For example,
We can see both graphs in teh figure below. Note some other cases here.
Important Notes on Exponential Graph:
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FAQs on Exponential GraphExponential graph is the graph of an exponential function. It always has a horizontal asymptote but no vertical asymptote. Graphing exponential function is the process of drawing the curve representing it. How to Graph Exponential Function?To draw an exponential graph, follow the steps mentioned below:
How Would an Exponential Graph of Growth look like?The exponential growth graph is always increasing if we see it from left to right. i.e., it always has a positive slope. An exponential function f(x) = ax shows growth if a > 1. What are the Asymptotes of Exponential Graph?An exponential graph has a horizontal asymptote (HA). The HA of an exponential function f(x) = ax + b is y = b. It doesn't have any vertical asymptote. Is an Exponential Graph a Parabola?No, the parabola is the equation of a quadratic function. The graph of an exponential function either starts slowly and increases rapidly or it is the other way round. What is the Difference Between Exponential Graph and Logarithmic Graph?Mathematically, the exponential function and the logarithmic function are inverses of each other. So their graphs are reflections of each other with respect to the line y = x. How Would an Exponential Graph of Decay look like?The exponential decay graph is always decreasing if we see it from left to right. i.e., it always has a negative slope. An exponential function f(x) = ax shows decay if 0 < a < 1. |