To find the vertical asymptotes of the function f(x) = 2x² + 3x + 10, we primarily need to determine the points at which the function is undefined. Vertical asymptotes typically occur at the values of x for which the denominator of a rational function equals zero and the numerator does not cancel out these factors.
In this case, we notice that f(x) is a polynomial function, which can be simplified as follows:
f(x) = 2x² + 3x + 10Since polynomials are defined for all real numbers and do not have any denominators, this function does not have any vertical asymptotes. In essence, there are no values of x that will cause f(x) to be undefined.
It’s important to remember that vertical asymptotes are only relevant in the context of rational functions, where you have a fraction. Thus, you can conclude that:
- No vertical asymptotes exist for the function
f(x) = 2x² + 3x + 10.
To further analyze the behavior of the function at infinity, one might typically explore horizontal or oblique asymptotes, but in terms of vertical asymptotes, this function is well-behaved across all values of x.