Question

Identify the vertical and horizontal asymptotes for f(x)=2x^2+4 over x^2-5x+6. Show ALL of your steps.

Answer 1

Vertical Asymptote: x=2

Step 1: Start by factoring the denominator of the function:

x^2 - 5x + 6

Step 2: Set the denominator equal to 0, so you get the equation:

x^2 - 5x + 6 = 0

Step 3: Factor the equation to get the solutions:

x = 2, 3

Step 4: The vertical asymptotes are located at:

x = 2

Horizontal Asymptote: y=4

Step 5: Recognize that the degree of the nominator is higher than the denominator (in this case 2 > 1), so the horizontal asymptote is the coefficient of the highest degree of the nominator

y = 4