1.
Which equation represents a nonlinear function? (1 point)
y = x + 7
y = 3x – 1
y = 3x2 + 1
y = x – 1/2
Is the answer "y = 3x - 1"?
Any equation with an exponent is non-linear
thank you!!!!!
That is not the answer. There is no exponent in that equation.
Is your third equation supposed to be
y = 3x^2 +1
To determine which equation represents a nonlinear function, we need to understand the characteristics of linear and nonlinear functions.
A linear function is an equation that represents a straight line when graphed. It has a constant rate of change, meaning that as one variable increases or decreases, the other variable also changes at a constant rate. Linear functions can be written in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.
On the other hand, a nonlinear function does not have a constant rate of change and does not form a straight line when graphed. The equation of a nonlinear function generally involves exponents, roots, or other non-linear operations.
Looking at the given equations:
1. y = x + 7: This equation is linear because it is in the form y = mx + b, and it represents a straight line when graphed.
2. y = 3x - 1: This equation is also linear. It follows the form y = mx + b, representing a line with a slope of 3 and a y-intercept of -1.
3. y = 3x^2 + 1: This equation is nonlinear because it involves an exponent (x^2), making it a quadratic function. When graphed, it forms a U-shaped curve.
4. y = x - 1/2: This equation is linear because it follows the form y = mx + b, representing a straight line with a slope of 1 and a y-intercept of -1/2.
Therefore, the answer is not "y = 3x - 1." The correct answer is "y = 3x^2 + 1" since it represents a nonlinear function.