Answer:
x = -1
x = -3
slant
Explanation:
Rational functions are formed by the quotient of 2 polynomials.
Vertical Asymtopes
The vertical asymptote of a rational function is a vertical line that separates the 2 sides of a rational function. The function cannot cross the vertical asymptote. This is because the vertical asymptote represents where the denominator equals zero. Since you cannot divide by 0, the function cannot be equal to the vertical asymptote. In this case, there is a drawn vertical asymptote at x = -1. You can see how neither side of the function ever crosses this line.
Point Discontinuity
Point discontinuities are also known as holes in a function. These form when the numerator and denominator both equal zero. These are also sometimes referred to as removable discontinuities because they can be removed by factoring or other methods. We can see that there is an undefined point at x = -3.
Slant Asymptotes
With rational functions, we can use asymptotes to describe end behaviors. In this case, the function does not approach a single value. Instead, it approaches a slanted line. This is known as a slant asymptote. Given the rational function, we can find the equation for the slant asymptote by using long division.