3r2 +5x1 3. Suppose q is the rational function defined by q(z)=321 5ed +7x +10 (

Question

3r2 +5x1 3. Suppose q is the rational function defined by q(z)=321 5ed +7x +10 (a) Determine the domain of q(x) and write the answer in interval notation (b) Determine the vertical asymptote(s), if any, of the graph of q(x). (Please makes sure to justify your answer.) behavior of the q(x) for z near +oo and for near -oo. That is, determine the horizontal asymptote of the graph of q(x). (Please explain or show work to justify your answer.) (e) Determine the (d) Determine the y-intercept of the graph of q(z)

Explanation / Answer

q = 3x^2 + 5x + 1 / (x^2 + 7x + 10)

Now, clearly b/w num and den, nothing cancels

So, we can write for domain :
x^2+ 7x +10 = 0
(x + 2)(x + 5) = 0
x = -2 and x = -5

Domain : (-inf , -5) U (-5 , -2) U (-2 , inf)

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b)
VA :
x = -5 and x = -2

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c)
Degrees of num an den are same
So, to find end behavior, we just divide the leading coefficients...

3/1

y = 3 --> HA

As x ---> inf, y ---> 3
As x --> -inf, y ---> 3

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d)
Plug in x =0 and find y....
y = 1/10

So, y-int is (0 , 1/10)

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