In order to determine which functions have a constant rate of change, we need to determine if the functions have the same rate of change for any given interval.
A constant rate of change means that for any interval on the graph, the ratio of the change in the dependent variable (usually denoted as y) to the change in the independent variable (usually denoted as x) remains constant.
Let's examine each function:
1) y = 3x + 2
This is a linear function in the form of y = mx + b, where m is the coefficient of x. The coefficient of x, which is 3 in this case, determines the rate of change. Since it is constant, this function has a constant rate of change.
2) y = x^2 + 4
This is a quadratic function. The rate of change for a quadratic function is not constant. It depends on the value of x.
3) y = 5x^3 + 2x
This is a cubic function. Similar to quadratic functions, cubic functions do not have a constant rate of change. The rate of change depends on the value of x.
4) y = sqrt(x)
This is a square root function. Like quadratic and cubic functions, square root functions do not have a constant rate of change.
Therefore, the function with a constant rate of change is y = 3x + 2.
Below, there are four functions. Select the functions with a constant rate of change.
(2 points)
1 answer
1 answer