Question

Please answer last oneFind the oblique asymptote, if there are anyA. Y=B. There are no

Answer 1

Explanation:

An oblique asymptote is a slanted line that the function approaches as x approaches ∞ or -∞ .

Thus, the equation for an oblique asymptote with slope m and y-intercept b will be:

$y=mx+b$

Consider the following graph:

According to this picture, there is an oblique asymptote that passes through the points (X2, Y2)=(2,-4) and (X1, Y1) = (0,0). Then, the slope m of this asymptote is:

$m=\frac{Y2\text{ -Y1}}{X2\text{ -X1}}=\frac{\text{ -4 -0}}{2\text{ -0}}=\text{ }\frac{\text{ -4}}{2}=\text{ -2}$

Now, notice that the oblique asymptote that passes through the origin, thus the y-intercept of this line would be

$b=0$

then, the equation for the oblique asymptote is:

$y=\text{ -}2x$

we can conclude that the correct answer is:

Answer:$y=\text{ -}2x$