Suppose a function, f(x) has a vertical asymptote toward positive infinity at x= -1,
A horizontal asymptote at y = 1=2 as x �¨�}�‡1, and a turning point at (1;-1). Sketch what you think the function would look like.
To sketch the function, we need to use the given information about the behavior of the function at various points.
1. Vertical Asymptote:
The vertical asymptote is at x = -1, which means that as x approaches -1 from both sides, the function gets arbitrarily close to positive infinity or negative infinity. We can represent this by drawing a vertical dashed line at x = -1.
2. Horizontal Asymptote:
The horizontal asymptote is at y = 1/2. As x approaches positive infinity or negative infinity, the function approaches the value of 1/2. We can represent this by drawing a dashed line at y = 1/2.
3. Turning Point:
The function has a turning point at (1, -1). This means that the function changes direction at this point and goes from decreasing to increasing or vice versa. We can represent this by sketching a curve that changes direction at the point (1, -1).
Combining these pieces of information, we can draw a graph. We start with a curved line that approaches the vertical asymptote at x = -1. As we move further away from x = -1, the curve approaches the horizontal asymptote at y = 1/2. Finally, at (1, -1), the curve changes direction. The sketch should resemble an "S" shaped curve with a vertical asymptote at x = -1, a horizontal asymptote at y = 1/2, and a turning point at (1, -1).
Please keep in mind that the sketch provided is an approximation based on the given information. The actual function may differ in terms of the specific shape and behavior.