f(x)=e^2x-1 +3
**(2x-1) is the power**
what is the equation of asymptote
as x -> -∞ e^(2x-1) -> 0
So, f(x) -> 3
You know what exponential curves look like. They all have y=0 as the asymptote. Then you can shift them up and down if you like. In this case, it is shifted up by 3.
Write an equation to a polynomial with the following properties and sketch. Fourth degree equation, lead coefficient is -2, two negative real roots and one positive real root, the positive real root has multiplicity of 2.
To find the equation of the asymptote, we need to determine if the function has a horizontal asymptote or a vertical asymptote.
First, let's check if there is a horizontal asymptote. For rational functions, we look at the degrees of the numerator and denominator to determine the presence and location of horizontal asymptotes. However, our given function is not a rational function but an exponential function.
In the case of exponential functions, such as the one given, there is no horizontal asymptote. Exponential functions grow without bound as x approaches positive or negative infinity.
Hence, the equation of the asymptote for this function is not applicable or non-existent.