# Advanced Mathematical Functions Worksheets

We all understand that when we evaluate a function, we are simply replacing a variable with a given value. The types of functions that we are exploring in this section take the next step when we start to introduce you to inserting expressions with in already established expressions or equations as a result of evaluating functions. Therefore, we term these mathematical functions as advanced. This webpage features a massive series of lesson and worksheets that help students tackle upper-level functions from all aspects. The best way to approach these types of problems is to do your best to maintain a high level of organization and make a few sidenotes as you make your way through the problems.

### Aligned Standard: HSF-IF.A.2

- An f(x) Input-Output Table Step-by-step Lesson- We slowly advance you forward with this skill. Sometimes it can be a bit overwhelming.
- Guided Lesson - Exponents and roots get more involved with this set.
- Guided Lesson Explanation - I kind of expect students to have mastered algebraic operations at this point when explaining the value.
- Practice Worksheet - This worksheet might take students a good stretch of time. Remember each problems has three to four parts to it.
- Matching Worksheet - Match the starting tables to the final outcomes. This is set up so that students can easily follow it.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

These problems really start spreading to higher levels of thought.

- Homework 1 - Use the function table to complete all the outputs.
- Homework 2 - To evaluate expressions with square roots, first simplify the quantity under the square root and take the square root. Then perform any other operations.
- Homework 3 - The first x-values into the tables.

### Practice Worksheets

We always recommend that you have students write a small outline of the steps they are going to take to solve the problem before they start.

- Practice 1 - Notice that they end in f (z) and f (x) values.
- Practice 2 - Use the following function rule to find f (170).
- Practice 3 - More table work for you.

### Math Skill Quizzes

The quizzes in this section might take a little extra time than previous work.

- Quiz 1 - This is a full on review of all the content here.
- Quiz 2 - What is the missing piece here?
- Quiz 3 - A solid way to end this worksheet section.

### What Are f(x) Input-Out Tables?

Input and output tables are not a new concept in algebra. These refer to the diagrams that help in identifying the basic functions. These tables are commonly used to find out the pair of coordinates that are based on the rule of the function. As you fill in the tables, a coordinate pair is produced that helps in constructing the graph. Here, the value of x is the input, applied to the function whereas the output is f(x), or the answer you will get when you substitute the value of x into the function.

In input-output tables, the function is mostly represented by f(x) rather than y. This shows that f is a function of x. This is simplified with the help of input-output tables. Looking at the first input, the output yield will be 1 with method 3(0) + 1 = 1. Taking the second input as 1, the second output will be 4, and like this, all the outputs can be achieved and plotted on a graph.

### Advanced Mathematical Functions in the Real World

Input-out tables are the basics of working with functions. You put this in and that is what you will get out it. It is elegant and concrete. There is no wiggle room. If you meet a certain condition this is what will be the result. It reminds of the Box Tops for Education program. This is where when you collect enough points, they give you a fixed prize based on what you have accumulated. Almost all reward programs that companies have created follow a function of some sort. This is good for both the customer and the business because they have a clear and concise linear path to what is required for both of them. In a way, functions are the mathematical equivalent of real-world contracts. A contract details the legally required actions of all parties that are entering the agreement. It sounds a great deal like a mathematical function, doesnâ€™t it? This section of our site looks at more advanced problems where will either include expressions as the variable or involve some form of sophisticated math.