Question

Graph the limit of a function calculator.

A) Horizontal asymptote
B) Vertical asymptote
C) Point of discontinuity
D) Critical point

Answer 1

The graph of a function can provide information about its characteristics such as horizontal asymptote, vertical asymptote, point of discontinuity, and critical points.

Step-by-step explanation:

The graph of a function can provide information about its characteristics. In this case, we are looking for the horizontal asymptote, vertical asymptote, point of discontinuity, and critical points. Let's define each of these:

1. Horizontal asymptote: This is a horizontal line that the graph approaches as x tends to positive or negative infinity. To find the horizontal asymptote, we need to determine the behavior of the function as x approaches infinity or negative infinity.
2. Vertical asymptote: This is a vertical line that the graph approaches as x approaches a certain value. To find the vertical asymptote, we need to determine the behavior of the function as x approaches a specific value.
3. Point of discontinuity: This is a point at which the function is not defined or has a jump, hole, or vertical tangent. It indicates a break or gap in the graph of the function.
4. Critical point: This is a point where the derivative of the function is zero or undefined. It represents a potential maximum, minimum, or inflection point.

To graph these characteristics, we need to analyze the function, its behavior at infinity and specific values, and its derivative if applicable.