I need help on graphing..

Question

How would I graph this function:

f(x)=[x^2-3x]/[x+4]

 

 

Answer 1

x-intercepts: y=0 (Means find the values of x for which the numerator of the fraction is zero):

 

x^2 - 3x = 0

 

x (x - 3) = 0

 

x₁ = 0 and x₂ = 3

 

There are 2 x-intercept points: (0,0) and (3,0).

 

y-intercept: x=0 (Replace x with zero, and calculate the value of y):

 

y = [0^2 - 3*0]/[0 + 4] = 0

 

One y-intercept point (same as one of the x-intercepts): (0,0).

 

Vertical Asymptotes: Denominator of the fraction equal zero:

 

x + 4 = 0

 

One vertical asymptote: x = -4.

 

Horizontal or Slant Asymptotes : The quotient of the actual division (ignore the remainder).

 

[x^2 - 3x]/[x + 4] = Quotient(x - 7) + Remainer(28)/Denominator(x+4)

 

Quotient depends on x, so we have slant asymptote y = x-7.