Unit 3 lesson 11 comparing function
In mathematics, comparing functions involves analyzing various properties of the functions, such as their rates of change, growth, shapes, and values. When comparing functions, we usually explore the following aspects:
1. Domain and range: The domain of a function is the set of all possible input values or x-values, while the range is the set of all possible output values or y-values. When comparing functions, you can check if they have the same domain and range or if there are any differences.
2. Increasing/Decreasing: We can compare functions by looking at their rates of change, i.e., if the function is increasing or decreasing in specific intervals of their domain. This can help us understand the overall behavior of the functions.
3. Intercept(s): Knowing where a function intersects important axes (x-axis or y-axis) gives insight into their behavior. Comparing x-intercepts and y-intercepts tells us how functions may behave around these points.
4. Asymptotes: Functions can have asymptotes, which are lines that they approach but never actually touch. Comparing asymptotes of different functions can also provide insight into their behavior.
5. End behavior: Comparing end behavior means looking at what happens to the functions as the input values (x) approach infinity or negative infinity. It can help us understand the long-term behavior of functions.
6. Parent Functions and Transformations: Many functions are transformations of known functions called parent functions. By comparing the parent functions and identifying the transformations, we can understand the relation between two functions better.
7. Graphical Analysis: Analyzing the graphs of functions can provide a visual way to compare them. By looking at the graph, we can understand the behavior of the functions, their steepness, and other properties.
In summary, when comparing functions, we look into various aspects such as domain, range, rates of change, intercepts, asymptotes, end behavior, parent functions, and graphical analysis to understand and analyze the similarities and differences between two or more given functions.