Question

I have a question on how to sketch a graph...

Answer 1

i figured out the derivatives but how do i get the x-int y-int?

Answer 2

X-intercepts occur when y=0 (touches the x-axis)
Y-intercepts occur when x=0 (touches the y-axis)

Answer 3

put x=0, and get y for for the value of y-int. viceversa for x-int.

Answer 4

for the numerator or denominator?

Answer 5

what about horizontal asymptote?

Answer 6

This refers to the y and x in
y = 1/(x-2) - 3
Try evaluating for when y=0 and when x=0 and solve for the other variable. Those will be the intercept points (x,0) and (0,y) (respectively.)

Answer 7

We could either use the fact that 1/(x-2) is a shift to the right of 1/x and that we know 1/x has horizontal asymptote y=0...

or we could look at the function as a quotient of two polynomials and only look at the leading terms and their degrees.
when the degree of the numerator is less than or equal to the degree of the denominator, there is a horizontal asymptote.
* equal => (numerator leading coefficient)/(denominator leading coefficient)
* less than => y=0