The vertical asymptotes are: "x = 3" and "x = -3" .
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The horizontal asymptote is: "y = 2" .
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Explanation:
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f(x) = $\frac{x^{2}+ 3}{ x^{2} - 9}$ ;

We know that "(x² − 9) ≠ 0 ; since we cannot divide by "0" ; so the "denominator" in the fraction cannot be "0" ;

since: 9 − 9 = 0 ; "x² " cannot equal 9.

So, what values for "x" exist when "x = 9" ?

x² = 9 ;

Take the square root of EACH SIDE of the equation ; to isolate "x" on one side of the <span>equation ; and</span> to solve for "x" ;

√(x²) = √9 ;

x = ± 3
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So; the vertical asymptotes are: "x = 3" and "x = -3" .
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The horizontal asymptote is: "y = 2" .
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(since: We have: </span>f(x) = $\frac{x^{2}+ 3}{ x^{2} - 9}$ ;

The "x² / x² " as the highest degree polymonials; both with "implied" coefficients of "1" ; and both raised to the same exponential power of "2".

6 0

3 years ago

The x intercept of the line is ___, and it’s y intercept is ___.

matrenka [14]

Answer:

The x-intercept is 5 and the y-intercept is 20. To find the x-intercept plug in y = 0 into the equation and then solve for y and to find the y-intercept plug in x = 0 into the equation and solve for y.

5 0

3 years ago