Chapter 11, Problem 2CR

To determine

Choose the correct term to complete the sentence.

Answer to Problem 2CR

As x and y gets larger in absolute value, the graph of the function gets closer to the line $a(n)$ called an Asymptote.

Explanation of Solution

Given:

A line that the graph of a function gets closer to as x or y gets larger in absolute value is $a(n)$ $\underleftarrow{?}$

Concept Used:

 An asymptote of a curve is a line which is tangent to the curve at a point at infinity. For curves given by the graph of a function $\text{y}\text{=}\text{f}\text{(x)}$ , horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to + 8 or - 8.

An asymptote of the curve $\text{y}\text{=}\text{f}\text{(x)}$ or in the implicit form: $\text{f}\text{(x,}\text{y}\text{)}\text{=}\text{0}$ is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity.

As x and y gets larger in absolute value, the graph of the function gets closer to the line $a(n)$ called an Asymptote.

Thus, as x and y gets larger in absolute value, the graph of the function gets closer to the line $a(n)$ called an Asymptote.