f(x)=4x^2/x(2x+1). draw the graph and find the HA and VA

Question

i need the answer asap

Answer 1

First, the graph simplifies down to:

^4x/_{2x + 1}

However, when we graph it, you're going to need to put a small circle at where the line crosses at (0,0). Just because an x was factored and cancelled out doesn't mean that it doesn't still have an effect (put x = 0, and the denominator will be undefined)

 

With that +1 constant in the denominator, the graph essentially shifts its VA to the left one unit, so the VA will be at x = -1.

 

For the HA, we take a look at the highest power of x and compare the coefficients:

^4x/_2x

4 ÷ 2 = 2, so the HA will be at y = 2.

 

To tell which directions the graph are hugging the asymptotes, plug in a number close into them. (x = -1.1, -0.9, 100, and -100, and find for y.)