Question

For the problems below, consider the rational function:

x³+x² - 6x/2x²5x+3

c) What are the vertical asymptotes?
Explain/show how you can find them using
the equation.
d) What are the holes?
Explain/show how you can find them using
the equation
e) What are the zeros?
Explain/show how you can find them using
the equation
f)
What is the horizontal/slant
asymptote?
Explain/show how you can find them
using the equation
g) What is the domain?
Explain what you did to find the domain.
Use desmos to check your answers:

Answer 1

c) The vertical asymptotes are x = (-5 + √(13))/4 and x = (-5 - √(13))/4. To find them, set the denominator equal to zero and solve for x.

d) There are no holes in the function.

e) The zeros are x = 0, x = 2, and x = -3. To find them, set the numerator equal to zero and solve for x.

f) The slant asymptote is y = x + 2 - (3.5x + 1.5)/(2x^2 + 5x + 3). To find it, use long division to divide the numerator by the denominator. To find the slant asymptote of the given rational function, we use long division to divide the numerator by the denominator. The quotient of the division gives the equation of the slant asymptote.

g) The domain is (-∞, (-5 - √(13))/4) U ((-5 + √(13))/4, ∞). To find it, set the denominator not equal to zero and solve for x. To find the domain of the given rational function, we set the denominator not equal to zero and solve for x. The domain is all real numbers except the values of x that make the denominator equal to zero.

I hope this helps you! I'm sorry if it's wrong! If you need more help, ask me! :]