I am having trouble in this class and need help with this question..
What similarities and differences do you see between functions and linear equations studied Are all linear equations functions? Is there an instance in which a linear equation is not a function?
(I understand that a function is a correspondence between a first set, called the domain, and a second set, called the range, such that each member of the domain corresponds to exactly one member of the range. And Linear equations can have more than one variable.)
How do you tie the main differences together?
I have to create an equation of a nonlinear function and provide two inputs for your classmates to evaluate.
This is the example given by my teacher..
A function must have each member of the domain (x value) mapped to only 1 value of the range (y value). For example,
(1,5)(2,6)(3,7)(4,8)(5,8)
Domain range
1 5
2 6
3 7
4 8
5 8
How do I create an equation of a non-linear function?
y=x^2 is a non-linear function.
linear is a straight line such as y=ax+b while y=ax^2+bx+c is non linear. a function is defined as each x value giving a unique y value. I'll leave you to take it from here, hope this helped.
To create an equation for a non-linear function, you need to consider a relationship where the output values (range) do not have a constant rate of change with respect to the input values (domain). Unlike linear equations, non-linear functions can have curves or irregular patterns in their graphs.
One way to create an equation for a non-linear function is by using a quadratic equation. A quadratic equation is a second-degree polynomial equation, represented in the form of y = ax^2 + bx + c, where a, b, and c are constants. In this case, the graph of the function will be a parabola.
To provide two inputs for your classmates to evaluate, you can choose two values for the x variable and substitute them into the equation to find the corresponding y values. Let's consider the example of the quadratic function y = x^2:
If you select x = 2, you can substitute it into the equation:
y = (2)^2 = 4
So, for x = 2, the corresponding y value is 4.
Similarly, if you choose x = -3:
y = (-3)^2 = 9
So, for x = -3, the corresponding y value is 9.
Now, your classmates can evaluate the non-linear function by substituting different values of x into the equation and finding the corresponding y values.