Discrete Function Worksheets
Mathematical functions are used to model inputs and predicated outputs. If those input and output values are set or fixed rather than spanning an interval, we refer to it as a discrete function. Because the values found within these sets are fixed and not flowing continuously, they end having gaps or holes within them when you graph them. They simply do not appear to be uniform when you graph them and since they are not continuous, we do not connect them with a line. When we are modelling real world problems, discrete functions are very useful for modelling anything that revolves around counting. These lessons and worksheets have students learn all the necessary steps to take to find the inverse of a given discrete function.
Aligned Standard: HSF-BF.B.4a
- Inverse Exchanges Step-by-step Lesson- We want to make these values run along the opposite axis when graphed.
- Guided Lesson - Find the inverse of all the functions along the way.
- Guided Lesson Explanation - I specifically chose function that would work out nicely, hence the title.
- Practice Worksheet - Some people, even teachers, get thrown by the notation. We are still looking for just the inverse.
- Matching Worksheet - Match the functions to their inverses.
- Answer Keys - These are for all the unlocked materials above.
Homework Sheets
Make sure that students get very comfortable with the vocabulary here before setting them loose on their own.
- Homework 1 - An inverse relation is when you change the variables in such a way that they go along the opposite axis.
- Homework 2 - To find the inverse exchange first write the function in terms of y and then solve for y.
- Homework 3 - The general rule that you follow for inverses of points is to switch the x and y values.
Practice Worksheets
The inverse exchange concept does throw a few children off. Make sure they understand it.
- Practice 1 - Find the inverse exchange. If f = {(9, 3), (-7, -2), (4, -2), (7, 3)} Find f-1(x)
- Practice 2 - Sometimes it only require you to just flip the x and y.
- Practice 3 - Complete the following problems.
Math Skill Quizzes
Sometimes the inverse of a function can be simple. Other times, it can take 30 minutes.
- Quiz 1 - There will always be a need to square both side of the equation.
- Quiz 2 - The matching problems serve as a good introduction to this quiz.
- Quiz 3 - Find the inverse of the function. If f(x) = √x + 23. Find f-1(x)
What are Discrete Functions?
We know the mathematical functions are rules, expression, and sometimes laws that establish a relationship between input and output variables. There is a specified singular output for every input. The domain of function are all of the values that are allowed to be plugged into the function. The range of a function are all the acceptable outputs of it.
A set of functions that are not continuous and can only take up certain values are known as discrete functions. Their domain and range are set in a discrete set of values. More simply put, discrete functions are functions with distinct and separate values. This explains that the values of these functions are not linked or connected with each other. It can also be explained as a set of values that can be listed. It explains and represents numbers that can be counted, for example, a list of integers or a set of whole numbers. Because of these properties discrete function have a very noticeable points and gaps found within their graphs. Consider an example to understand better. Let's say that you have a list of numbers ranging from 1 to 10. The discrete function can equal 1, 2, 3, 4 and so on but it does not represent 1.2, 2. 5, 3.5 or any other linking number.
When a function displays continuous properties across its domain or intervals within that domain it is referred to as non-discrete. As a result, graphs of non-discrete functions lack any breaks, gaps, or holes within them. We can often just take a look at the graphs of these functions to be able to accurately describe their nature.