# Comparing Linear Functions and Equations and Domain & Range

(1)- What similarities and differences do you see between functions and linear equations that you studied in Chapter 3?

. Are all linear equations functions?

· Is there an instance in which a linear equation is not a function? Support your answer.

· Create an equation of a nonlinear function and provide two inputs for your classmates to evaluate.

· Find examples that support or refute your classmates' answers to the discussion question. Provide additional similarities and differences between functions and linear equations. Challenge your classmates by providing more intricate examples of nonlinear functions for them to solve.

(2)- What is the difference between domain and range?

· Describe a real life situation that could be modeled by a function.

· Describe the values for x that may not be appropriate values even when they are defined of your classmates' function. A function could, for example, indicate the amount of bone strength (y) in a living human body over time in years (x). It would not make sense to look at negative years, because the person would not yet be born. Likewise, looking beyond 100 years might not make sense, as many people do not live to be 100.

#### Solution Preview

1. What similarities and differences do you see between functions and linear equations? Are all linear equations functions? Is there an instance when a linear equation is not a function? Support your answer. Create an equation of a nonlinear function and provide two inputs for someone to evaluate.

A function is almost always confused with an equation and most students of Math may not appreciate a very clear distinction between the two. An equation has no special notation to identify it, whereas a function is denoted by letters such as f, g, h, , F etc.

[If we have only one function to discuss, we usually use the notation “f” meaning “function”]

Consider f(x) = 8x + 5

This is a linear function. You can think of a function as a machine that takes in a number, does some sort of work on it, and puts it out as another number at the other end of the machine. In this case, you put in some number x; the function multiplies it by 8, then adds 5 to the result, and puts out this new number, which is called f(x).

If you give that new ...

#### Solution Summary

The similarities and differences between functions and linear equations are given. The solution discusses domain and range.