what is true about the function y = (2x² - 3x + 7)/(x - 4)? the function has a horizontal asymptote at y =…

what is true about the function y = (2x² - 3x + 7)/(x - 4)? the function has a horizontal asymptote at y = 2. the function has no asymptotes. the function has a horizontal asymptote at y = 0. the function has an oblique asymptote at y = 2x + 5.

what is true about the function y = (2x² - 3x + 7)/(x - 4)? the function has a horizontal asymptote at y = 2. the function has no asymptotes. the function has a horizontal asymptote at y = 0. the function has an oblique asymptote at y = 2x + 5.

Answer

Answer:

D. The function has an oblique asymptote at $y = 2x + 5$.

Explanation:

Step1: Perform polynomial long - division

Divide $2x^{2}-3x + 7$ by $x - 4$.

Step2: Set up long - division

$\frac{2x^{2}-3x + 7}{x - 4}=2x+5+\frac{27}{x - 4}$.

Step3: Analyze the result

As $x\to\pm\infty$, $\frac{27}{x - 4}\to0$. So the oblique asymptote is $y = 2x+5$.