Given [math]f(x)=\frac{\textcolor{blue}{a}{x}\textcolor{red}{^m}{-2x+5}}{\textcolor{magenta}{b}{x}\textcolor{#006400}{^n}{+4x-1}}[/math], how does the function behave as [math]x[/math] becomes arbitrarily large, or negatively infinite (i.e. as [math]x[/math] approaches ±∞)? Experiment by adjusting the [b]degree[/b] and [b]leading coefficients[/b]. [You can "zoom out" if need be.]

Things to consider: 1. How does the function behave if [color=#c51414][b][i]m[/i][/b][/color] and [color=#0a971e][b][i]n[/i][/b][/color] are equal? 2. What role do the leading coefficients have in the function's end behaviour? 3. How does the function behave if [color=#c51414][b][i]m[/i][/b][/color] is greater than [color=#0a971e][b][i]n[/i][/b][/color]? 4. How does the function behave if [color=#c51414][b][i]m[/i][/b][/color] is less than [color=#0a971e][b][i]n[/i][/b][/color]? 5. [Challenge] How does the function behave if [color=#c51414][b][i]m[/i][/b][/color] is one more than [color=#0a971e][b][i]n[/i][/b][/color]?