Which of the following gives an example of a function that is not linear?(1 point)%0D%0AResponses%0D%0A%0D%0Ay=x2−3x+2.25%0D%0Ay equals x squared minus 3 x plus 2.25%0D%0A%0D%0A2x+3y=16%0D%0A2 x plus 3 y equals 16%0D%0A%0D%0A9x+3y−18=0%0D%0A9 x plus 3 y minus 18 equals 0%0D%0A%0D%0Ay=16x+23
To determine which of the given options represents a function that is not linear, we need to understand the characteristics of a linear function.
A function is considered linear if it has a constant rate of change, meaning that the change in the dependent variable (y) is constant for every unit change in the independent variable (x). In other words, the graph of a linear function forms a straight line.
Let's analyze each option:
1) y = x^2 - 3x + 2.25
This is a quadratic function since it includes an x^2 term. Quadratic functions are not linear.
2) 2x + 3y = 16
This is a linear equation in standard form. To determine if it is a function, we can isolate y and check if there is only one y-value for each x-value.
Converting the equation to slope-intercept form (y = mx + b):
3y = -2x + 16
y = (-2/3)x + 16/3
Since it represents a straight line, this equation is a linear function.
3) 9x + 3y - 18 = 0
This is a linear equation. Similar to the previous step, we can manipulate the equation to isolate y:
3y = -9x + 18
y = (-9/3)x + 6
Again, this equation represents a straight line, making it a linear function.
4) y = 16x + 23
This equation is in slope-intercept form, which is a common way to represent linear functions. Since it represents a straight line, it is a linear function.
Therefore, the example of a function that is not linear is option 1: y = x^2 - 3x + 2.25.