Answer:
A function with a slant asymptote (also known as an oblique asymptote) and a hole, but no vertical asymptote and is not a line can be represented by a rational function with a numerator and denominator of appropriate degrees.
Here's an example:
f(x)= x
2
−1
x
3
−2x
2
−x+2
In this function:
1. It has a slant asymptote because the degree of the numerator (3) is one greater than the degree of the denominator (2). The slant asymptote represents the long-term behavior of the function as x approaches positive or negative infinity.
2. It has a hole at x = 1 because both the numerator and denominator have a common factor of (x - 1), which can be canceled out. This creates a hole at x = 1.
3. It does not have a vertical asymptote because the denominator does not equal zero for any real value of x, except for the value that was canceled out to create the hole.
4. It is not a line because it's a rational function with a non-constant numerator and denominator.
You can graph this function to see how it behaves, including the slant asymptote and the hole.
Explanation:
if you need a personal homework helper dm me on ig, savant.carlos