Question

How do you find the vertical asymptote of exponential function?

Answer 1

Hint:In order to determine the vertical asymptote of exponential function, consider the fact that the domain of exponential function is $x \in \operatorname{R} $.So there is no value of x for which y does not exist . So no vertical asymptote exists for exponential function.

Complete step by step solution:
Let’s assume an exponential function $f(x) = {a^x}$where x is the variable.
So let's find the domain for x, for exponential function the domain is $x \in R$where R is the set of Real numbers.
Hence, therefore there is no vertical asymptote of exponential function (as there is no value of x for which it would not exist).
But if we talk about the horizontal asymptote it exists at $y = 0$as$\mathop {\lim }\limits_{x
\to
\infty } {a^x} = 0$

Therefore, the answer is no vertical asymptote exists for exponential function.

Additional Information: 1.Cartesian Plane: A Cartesian Plane is given its name by the French mathematician Rene Descartes who first used this plane in the field of mathematics .It is defined as the two mutually perpendicular number line , the one which is horizontal is given name x-axis and the one which is vertical is known as y-axis. With the help of these axis we can plot any point on this cartesian plane with the help of
ordered pair of numbers.

2.Vertical asymptotes for rational functions are found by setting the denominator equivalent to 0. This additionally assists with finding the domain. The domain can NOT contain that number

3.Horizontal asymptotes are found by subbing in huge positive and negative qualities into the function. $f(1000)$ or $f(1000000)$can assist with figuring out where the function "closes" are going. $\mathop {\lim }\limits_{x \to \infty } f(x)$

Note: 1.Draw the cartesian plane only with the help of straight ruler and pencil to get the perfect and accurate results.

2.You can take any two points from the equation to plot the graph to the equation