Find the horizontal intercepts, etc

Question

Find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph.



Answer 1

First you have to factor the numerator and denominator, this will give you

b(x) = (x-3)(x+2)/(x+2)(x-2) = (x-3)/(x-2) and since x+2 was originally in the denominator, the function will have a hole at (-2, 1.25).

For vertical intercept, plug in x =0 to get (0, 1.5)

for horizontal intercept, look at the numerator and set x -3 =0 so (3,0) is the intercept.

To find the horizontal intercept take the lim b(x) as x--->infinity so b(x) ~ x/x = 1 making the horizontal asymptote Y= 1

Heres my sketch of the graph: https://imgur.com/a/ikZ2AVh

Answer 2

Hi Ooyeon O.

Factor the numerator and denominator.

x cannot be positive two this is an asymptote, a vertical asymptote

y - intercept (0, 3/2)

x - intercept (3, 0)

y = 1 is a horizontal asymptote

There are no slant asymptopes since the exponent of the numerator is the same as the one in the numerator

You can check with at a graph.

Hope this helps