Chapter 2 homework ### Understanding Rational Functions through Graphs**Instructions:**Use the graph of the rational function to complete the following statement.**Given:**1. \( \text{As } x \rightarrow 3^+ \), \( f(x) \rightarrow \_\_\_\_\_\_\_\_ \)2. \( \text{As } x \rightarrow 3^- \), \( f(x) \rightarrow \_\_\_\_\_\_\_\_ \)**Graph Details:**The graph shown is a plot of a rational function. It includes vertical and horizontal asymptotes to guide your understanding of the function's limits and behavior.- **Graph Explanation:**The graph is a plot with both vertical and horizontal axes ranging approximately from -10 to 10. The rational function is indicated by a smooth curve in blue color. Key features of the graph include three asymptotes: - **Horizontal Asymptote:** \( y = -3 \) - **Vertical Asymptotes:** \( x = -3 \) and \( x = 3 \)Asymptotes are shown as dashed lines. The purple curves on the graph approach the asymptotes but never touch them, indicating how the function behaves as it nears these critical values.**Function Behavior Analysis:**To complete the given statements:1. To determine the behavior of \( f(x) \) as \( x \) approaches \( 3 \) from the right (\( 3^+ \)): - The graph shows that as \( x \) nears 3 from the right, the function \( f(x) \) trends towards positive infinity.Therefore, \[ \text{As } x \rightarrow 3^+ \), \( f(x) \rightarrow \infty \]2. To determine the behavior of \( f(x) \) as \( x \) approaches \( 3 \) from the left (\( 3^- \)): - The graph clearly depicts that as \( x \) nears 3 from the left, the function \( f(x) \) trends towards negative infinity.Therefore,\[ \text{As } x \rightarrow 3^- \), \( f(x) \rightarrow -\infty \]By analyzing these trends, one can understand the behavior of the rational function as it approaches its vertical asymptotes.### Conclusion:Through the graphical representation of the rational function and its

Name: Chapter 2 homework ### Understanding Rational Functions through Graphs
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Chapter 2 homework ### Understanding Rational Functions through Graphs**Instructions:**Use the graph of the rational function to complete the following statement.**Given:**1. \( \text{As } x \rightarrow 3^+ \), \( f(x) \rightarrow \_\_\_\_\_\_\_\_ \)