Question

Let R(x) = ( 2x^2 − 8x + 6 ) / (x^2 + 6x + 8)

a) Find all x such that R(x) is undefined. Find all x such that R(x) = 0. Evaluate R(0). Graph R(x) indicating all vertical and horizontal asymptotes and x and y intercepts.

b) Find the intervals on which ( x^2 + 2x + 12 ) / (x − 2) ≥ 2x + 5.

Answer 1

The function is undefined where the denominator equals 0, the argument of an even indexed radical is less than 0, or the argument of a logarithm is less than or equal to 0.

x=2,x=4

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for xand solve for yy.

x-intercept(s): (3,0),(1,0)

y-intercept(s): (0,3/4)

The horizontal asymptotes by comparing the degrees of the numerator and denominator.

Vertical Asymptotes: x=2,4

Horizontal Asymptotes: y=2

No Oblique Asymptotes

2)

2)