Graph the rational function ?

Question

f(x)= -2x^2-2x+1 / 2x-2

Find the asymptote

and graph points as many as posssible

I need the points to make a graph: I keep trying to do this and get stuck

Answer 1

-2x^2-2x+1 / 2x+2 = -x-2 + [3 / (2x-2)]

Taking denominator =0, x = 1.

Therefore, asymptotes are x =1 and y= -x -2

find some points using x= -4, x=-0.5, x=0.5, x= 1.5, x=3, x=5.

using dy/dx tests, there will be a max point at (2.22, -5.44) and a min point at (-0.22, -0.55).

and there u go.

Answer 2

There is a vertical asymptote at x = 2 and a slaant asymptote at y = -x-2. The x-intercepts are approximately -1.35 and .34. There is a y-intercept at (0, -.5). There is an upper and lower branch to the function like a hyperbola. The upper branch swoops down from the 2nd quadrant, crosses the x-axis at about -1.35, reaches a minimum and turns back up passing through the y-axis at (0.-.5) and recrossesthe x-axis at about x = .34 and continues upward toward infinity getting closer and closer to the vertical asymptote.

The lower branch starts from -infinity and rises to a maxand then shoots downward to - infinity hugging the slant asymptote.

Draw the asymptotes 1st. This will greatly facilitate the sketching of the graph.

Answer 3

Graphing:  Input values for x and the result is y, or f(x)

Do this several times, minimum 4, and plot the points.

Do this as many times as you need to plot the points and then connect them to draw the graph.

The asymptote is where your result is undefined (when the denominator = 0)