Question

What are the equations of the asymptotes of the graph of the function mc015-1.jpg? x = –5, x = 2 and y = 3 x = –2, x = 5 and y = 3 x = 3, y = –5, and y = 2 x = 3, y = –2, and y = 5

Answer 1

Answer:

Step-by-step explanation:

Our aim is to conclude which of the answers presented are the asymptotes of the graph of the function $f(x)=\frac{3x^{2} -2x + 1}{x^{2} +3x -10}$.

We know that an asymptote is a line that delimits a function and gets infinity close to the function, but they never meet.

We can name asymptotes in several ways, as vertical, horizontal and oblique.

When we have a quotient between polynomials, we can say that exits a vertical asymptote, where the function is not defined, i.e, in the zero of its denominator.

The vertical asymptotes are the vertical lines corresponding to the values of x for which

Thus, we need to compute the zeros of the denominator of f in order to compute its vertical asymptotes.

Then:

$x^{2} +3x-10= 0\\(x-2)(x+5) = 0\\ x = 2  or x = -5$

Hence, our vertical asymptotes of $f(x)$ are $x = 2$ and $x = -5$.

When we have a function with a greater power in the numerator instead of denominator, to compute its horizontal asymptotes we need to compute the ratio between the coefficients of the greater exponent of the numerator and the coefficient of the greater exponent of the denominator.

Therefore our horizontal asymptotes are y = 3.

Answer 2

Answer:

The answer is B

Step-by-step explanation:

I took this on edg