# Comparing Functions in Different Forms Worksheets

When we are classifying a function there are four main things that we can base this on. Many times, it will be based on the number of elements that are present within the function. We can also classify them based on the nature of the equation that is located within the function. The range or scope of function itself lends to another set of names entirely. The domain which is all the possible inputs for a function can also led to its classification. This collection of worksheets and lessons will get students comfortable with understanding functions that are expressed in different formats. It will also help them learn to restate functions in different forms.

### Aligned Standard: HSF-IF.C.9

- Input-Output Versus a Graph Step-by-step Lesson- This is why so many industries have made set ways to display data.
- Guided Lesson - This is definitely a valuable skill to master when you are examining company stocks.
- Guided Lesson Explanation - Choosing just two points will usually settle it for you, but not always.
- Practice Worksheet - I stuck with the Input-Output and graph comparison because it is very commonly used on National exams.
- Matching Worksheet - This one is more concerned about the growth curves and not the values.

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

### Homework Sheets

Analyze tables and premade graphs to see and compare trends.

- Homework 1 - Two functions are represented in different ways. Which function grows faster for large positive values of x? We will walk you through a complete problem.
- Homework 2 - When compared to another set of data. Slop intercept form is defined as y= mx + b m = slope b = y-intercept (where the line cross the y-axis)
- Homework 3 - Find two points where x
^{1}is not equal to x^{2}for both functions. In this case they are represented by a data table and a graph.

### Practice Worksheets

The practice sheets add the concept of understanding the trends of the graphs.

- Practice 1 - From the two functions, which function grows faster for large positive values of x? You will compare a quadratic and linear function.
- Practice 2 - Which function is moving to the right faster? It may be better stated as which is moving less to the left.
- Practice 3 - The focus is on positive movement, please note that.

### Math Skill Quizzes

We tried to make these questions as black and white as possible. We didn't want to confuse students

- Quiz 1 - Compare these bad boys.
- Quiz 2 - The input-output table shows the x- and y-values of a quadratic function. See if you can some sense of this.
- Quiz 3 - One more to knock home the skill for yourself. Remind that when analyzing everything.

### How to Compare Functions in Different Forms?

Comparing functions is important because it helps us improve our concepts of functions. Furthermore, it also provides you multiple ways to solve a function rather than one. There are different types of functions that we regularly use in different formats. A function can either be in the form of an input-output table or the form of a graph or the form of an equation.

Let us take an example. Two contestants on the "Biggest Loser" are Sarah and Noah. Their weight-loss progress is stated below. Sarah's weight-loss progress is shown in the form of an equation, where t is the time in weeks, and W is her weight. W = 170 - 2.5t.

Noah's weight-loss is tracked as: 0 Week, 230 Weight (pounds) | 1 Week, 229 Weight (pounds) | 2 Week, 228 Weight (pounds) | 3 Week, 227 Weight (pounds) | 4 Week, 226 Weight (pounds)

If we consider the comparison of both contestants, you can see that Sarah's losing 2.5 pounds every week, while Noah is losing 1 pound every week. We can use a function to state this. The form that this function can take on comes across a long line of classifications. In addition to compare functions to data tables, we will often be called upon to compare graphs as well. It is a good habit to get into convert those lines into equations before you evaluate them.