Q:

[tex]f(x) \frac{x^{2}+x-12 }{x-4}[/tex]Domain:V.A:Roots:Y-int:H.A:Holes:O.A:Also, draw on the graph.

Accepted Solution

A:
Answer:* Domain all real value of x except x = 4* Vertical asymptotic x = 4* Roots are -4 and 3* Y-intercept is 3* No horizontal asymptotic* There is no holes * O.A is y = x + 5 doesn't cross the functionStep-by-step explanation:* ∵ f(x) =( x² + x - 12)/x - 4∵ x - 4 = 0 ⇒ x = 4∴ The domain of the function is all real number except x = 4* The vertical asymptotic is when denominator = 0∴ x - 4 = 0 ⇒ x = 4∴ The vertical asymptotic is x = 4* The roots of the function is the value of x when y = 0∴ x² + x -12 = 0 ⇒ (x + 4)(x - 3) = 0∴ x = -4 and x = 3∴ The roots are -4 and 3* Y-intercept means x = 0∴ f(0) = 0 + 0 - 12/0 - 4 = -12/-4 = 3∴ The y-intercept = 3* ∵ The degree of numerator is greater than the degree of denominator ∴ There is no horizontal asymptotic* ∵ The hole is the value of x which makes the denominator and the      numerator = 0∴ There is no holes in this function* to find O.A ⇒ x² + x -12 ÷ x - 4 = x + (5x - 12)/x - 4                                                   = x + 5 + 8/x - 4∴ The O.A is y = x + 5 To check if it will cross the function ⇒ (x - 4)(x + 5) = x² + x - 20Compare it with x² + x - 12 we will find -20 ≠ -12∴ It will not cross the function