domain:
v. a:
roots:
y-int:
h. a:
holes:
o. a:

also, draw on the graph.

* 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 function

Step-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 - 20

Compare it with x² + x - 12 we will find -20 ≠ -12

∴ It will not cross the function

32

step-by-step explanation:

the answer is d

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