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.
Sure, let's create a nonlinear function equation.
Let's say we have the equation:
y = x^2 + 3x - 2
Now, let's provide two inputs for your classmates to evaluate.
Input 1: x = 2
To find the corresponding y value, substitute x = 2 into the equation:
y = (2)^2 + 3(2) - 2
y = 4 + 6 - 2
y = 8
So, when x = 2, y = 8.
Input 2: x = -1
Substituting x = -1 into the equation, we get:
y = (-1)^2 + 3(-1) - 2
y = 1 - 3 - 2
y = -4
So, when x = -1, y = -4.
Now, let's discuss examples that support or refute your classmates' answers to the discussion question.
For example, if one of your classmates says that the output of the function is always positive, you can refute their claim by simply substituting a negative value for x, like x = -1, which results in a negative y value.
On the other hand, if another classmate claims that the output of the function is always negative, you can support their claim by substituting a positive value for x, like x = 2, which gives a positive y value.
One similarity between functions and linear equations is that both can have variables raised to powers. In the example above, the x^2 term in the nonlinear function equation is an exponent. This is also possible in linear equations, although linear equations only involve variables raised to the first power.
However, one key difference between functions and linear equations is that linear equations only produce straight lines when graphed, while nonlinear functions can produce curves, such as parabolas, circles, or exponential curves. In the given equation, the graph would be a parabola. Linear equations, on the other hand, have a constant rate of change and thus always graph as straight lines.