Determine whether the function is linear, constant, or neither
y = x3 - x2 + 8
a. Linear
b. Constant
c. Neither
I think it is neither
If t were linear it would be of form
y = m x + b
if it were constant it would be of form
y = b
it is in fact a cubic polynomial.
By the way we usually write exponents as:
y = x^3 - x^2 + 8
Oh, this function is definitely a bit of a clown! It's neither linear nor constant. It's actually a cubic function with some fancy arithmetic going on. So, c. Neither is the correct answer! Keep on solving those equations!
You are correct. The function y = x^3 - x^2 + 8 is neither linear nor constant. A linear function would have a constant rate of change, while this function has varying rates of change due to the presence of the squared and cubic terms. A constant function, on the other hand, would have the same output value for all input values, but this function produces different output values for different input values. Therefore, the function is neither linear nor constant.
To determine whether the given function is linear, constant, or neither, we need to understand the definitions of these terms.
1. Linear function: A function is linear if the degree of the variable(s) in the equation is always 1. In other words, if the exponents of all variable(s) are 1, the function is linear.
2. Constant function: A function is constant if the output value (y) remains the same regardless of the input value (x). In other words, if the equation does not contain any variable(s), the function is constant.
Now let's determine the type of function for the given equation:
y = x^3 - x^2 + 8
The equation contains variable(s) with exponents greater than 1, which means it is not a linear function. Additionally, it contains the variable "x", so it is not a constant function either. Therefore, the function y = x^3 - x^2 + 8 is neither linear nor constant.
So, your initial understanding is correct - the function is neither linear nor constant.