Question

Check pictureOn the graph below, move the two points to graph the slant asymptote for the function f(x)=4x2−52x+2

Answer 1

Given:

$f(x)=\frac{4x^2-5}{2x+2}$

We will graph the given function using the asymptote of the function

First, as the degree of the numerator is greater than the degree of the denominator, we will make a long division

$f(x)=(2x-2)+\frac{-1}{2x+2}$

So, the slant asymptote will be the following line:

$y=2x-2$

We will graph this line using the intercepts

x-intercept, when y = 0, x = 1

y-intercept, when x = 0, y = -2

So, the lines passes through the points (0, -2) and (1, 0)

The graph of he function will be as follows: