Test: Rate of Change - SAT MCQ

The slope of a linear function represents its rate of change.

Linear functions have a constant rate of change.

The rate of change of a function is equal to its slope, which is 5/1 in this case.

The rate of change of a function at a specific point is represented by the instantaneous rate of change or the slope of the tangent to the function at that point.

The average rate of change of a function on the interval [a, b] is given by (f(b) - f(a)) / (b - a).

The rate of change for a function is defined as the ratio of the change in the output to the change in the input. This is the slope of the function, which gives information about how fast the function is changing at a particular point.

The function y = -x² has a negative rate of change for all values of x. This is because as x increases, the value of the function decreases, so the slope (rate of change) is negative.

The average rate of change of a function over the interval [a, b] is defined as the ratio of the change in the output to the change in the input over the interval [a, b]. This is the same as the slope of the line connecting the two endpoints of the interval.

The instantaneous rate of change of a function at a point is given by its derivative.
Applying the product rule, we find that f'(x) = (2x)(3x - 2) + (x² + 1)(3) = 6x^2 - 4x + 3x² + 3.
Therefore, the instantaneous rate of change at x = 1 is
f'(1) = 6(1) - 4(1) + 3(1) + 3 = 5.

If the rate of change of a function is positive, this means that the function is increasing. This is because as the input increases, the output increases at a faster and faster rate.