Sketch the graph of each rational function showing all the key features. verify your graph by graphing the function on
the graphing calculator.
2. f(x) = (3x − 6)(x − 4) / x(x − 4)

The x-intercept is 2.

The function has no y-intercept.

The vertical asymptote of the function is x=0.

The horizontal asymptote of the function is x=0.

The function has hole at x=4.

Step-by-step explanation:

The given function is

Cancel out common factors.

(i) x-intercept.

Substitute f(x)=0, in the given function.

The x-intercept is 2.

(i) y-intercept.

Substitute x=0, in the given function.

The function has no y-intercept.

(iii) Vertical asymptote.

Equate the denominator equal to 0.

Therefore, the vertical asymptote of the function is x=0.

(iv) Horizontal asymptote.

If degree of numerator and denominator are same, then horizontal asymptote is

Therefore, the horizontal asymptote of the function is x=0.

(v) End behavior

(vi) holes

Equate the cancel factors equal to 0, to find the holes.

The function has hole at x=4.

were is the equation