1) Is the equation a linear function or nonlinear function?
Equation: y = 2x^3
A) Linear
B) Nonlinear
2) Is the equation a linear function or nonlinear function?
Equation: y = 0.5x - 1
A) Linear
B) Nonlinear
3) Is the equation a linear function or nonlinear function?
Equation: y = 5x + 3
A) Linear
B) Nonlinear
4) Is the equation a linear function or nonlinear function?
Equation: y = 3x^2 + 2
A) Linear
B) Nonlinear
1) To determine if the equation y = 2x^3 is a linear or nonlinear function, we need to check if it satisfies the definition of a linear function. An equation is considered linear if it is of the form y = mx + b, where m and b are constants. However, in this equation, we have a variable raised to the exponent of 3, which means it is not a linear function. Therefore, the answer is:
B) Nonlinear
2) In the equation y = 0.5x - 1, we can see that it is in the form y = mx + b, where m = 0.5 and b = -1. Since all the variables are raised to the power of 1, and there are no higher-degree terms, this equation is a linear function. Therefore, the answer is:
A) Linear
3) Similar to the previous equation, y = 5x + 3 is in the form y = mx + b, where m = 5 and b = 3. Just like before, all variables are raised to the power of 1, and there are no higher-degree terms. Hence, this equation is a linear function. Therefore, the answer is:
A) Linear
4) Let's analyze the equation y = 3x^2 + 2. In this case, we have x raised to the power of 2, indicating that it is not a linear function. Linear functions have variables raised only to the power of 1. Consequently, the given equation is a nonlinear function. Therefore, the answer is:
B) Nonlinear
non-linear: any power of x greater than 1.
linear: only x terms and constants included.