How do you graph f(x)=(x^2+3x+2)/(−3x−12) using holes, vertical and horizontal asymptotes, x and y intercepts?

zapri4j

zapri4j

Answered question

2022-09-19

How do you graph f ( x ) = x 2 + 3 x + 2 - 3 x - 12 using holes, vertical and horizontal asymptotes, x and y intercepts?

Answer & Explanation

Jamari Morgan

Jamari Morgan

Beginner2022-09-20Added 10 answers

f ( x ) = x 2 + 3 x + 2 - 3 x - 12

Using long division, we can rearrange the polynomial
f ( x ) = ( - 3 x - 12 ) ( - 1 3 x - 1 3 ) - 2 - 3 x - 12

f ( x ) = - 1 3 x - 1 3 - 2 - 3 x - 12

This means that your oblique asymptote is y = - 1 3 x - 1 3 which can be found by figuring out what happens when x approaches 0 and your horizontal asymptote is x=−4 after solving −3x−12=0 since your denominator cannot equal to 0.

To figure out your x and y intercepts, we let y=0 and x=0 respectively.

When x=0, y = - 1 6 so your y-intercept is ( 0 , - 1 6 )
When y=0, x=−2 and x=−1 so your x-intercepts are (−2,0) and (−1,0)

graph{(x^2+3x+2)/(-3x-12) [-10, 10, -5, 5]}

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