What similarities and differences do you see between functions and linear equations studied in Ch. 3? 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 your classmates to evaluate.

Question

•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.

Answer 1

I have no classmates and I didn't read your chapter 3.

All linear equations are functions. Good luck with the rest of your assignment. If you have more specific questions, please try again.

Answer 2

First, what is a function? In Cartesian mathematics, a function is an expression which, for any value of x, there exists one and only one value of y. A function can be either a straight line (linear) or a curvy line (non-linear).

If you look at a linear equation graphically, you will see a straight line, so all linear equations are functions.

A non-linear equation, such as y = x², is a function, though not a straight line, because for any value of x there exists one and only one value of y.

An example of a non-function would be y = ± x. In this case, for any value of y, there exists two values of x. Therefore, it is not a function.

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Hot water is heavier by volume than cold water.
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Answer 3

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

Answer 4

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