Question

What is the asymptote of the graph of h(x)=2x^2−5 ?

Answer 1

Answers:
The function has no vertical asymptotes
The function has no horizontal asymptotes

Explanation:
1- getting the vertical asymptotes:
Vertical asymptotes occur when the denominator of the given function tends to zero.
This means that we need to equate the denominator to zero and solve for the variable.
The denominator in our function is a constant equal to 1 which cannot be equated to zero (1 ≠ 0).

Therefore, we cannot solve for vertical asymptotes which means that our function has no vertical asymptotes

2- getting the horizontal asymptotes:
For a function to have a horizontal asymptote, the degree of the numerator must be equal to or lower than the degree of the denominator.
In our function:
The highest power of x in numerator is 2 ........> numerator is 2nd degree
The highest power of x in denominator is 0 ....> denominator is zero degree

This means that the condition of a horizontal asymptote is not satisfied. Therefore, the function has no horizontal asymptotes