Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Functions
Rational functions are expressions formed by the ratio of two polynomials. They can exhibit unique behaviors such as asymptotes, intercepts, and discontinuities. Understanding the basic structure of rational functions is essential for analyzing their graphs and transformations.
Recommended video:
Intro to Rational Functions
Transformations of Functions
Transformations involve shifting, stretching, compressing, or reflecting the graph of a function. For example, adding a constant to a function, like in h(x) = 1/x + 2, translates the graph vertically. Recognizing how these transformations affect the original function is crucial for accurately graphing the new function.
Recommended video:
Domain & Range of Transformed Functions
Asymptotes
Asymptotes are lines that a graph approaches but never touches. For rational functions, vertical asymptotes occur where the denominator is zero, while horizontal asymptotes indicate the behavior of the function as x approaches infinity. Identifying these asymptotes helps in sketching the graph and understanding its limits.
Recommended video:
Introduction to Asymptotes