Front

What is the average rate of change of a function?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

What type of function is represented by a straight line?

Back

Linear function.

Front

What type of function has a constant second derivative?

Back

Quadratic function.

Front

How do you calculate the average rate of change from x=a to x=b?

Back

Average rate of change = (f(b) - f(a)) / (b - a).

Front

What is the average rate of change of the function f(x) = 3x + 2 from x=1 to x=3?

Back

Average rate of change = (f(3) - f(1)) / (3 - 1) = (11 - 5) / 2 = 3.

Front

What is the average rate of change of the function f(x) = x^2 from x=1 to x=4?

Back

Average rate of change = (f(4) - f(1)) / (4 - 1) = (16 - 1) / 3 = 5.

Front

What type of function increases exponentially?

Back

Exponential function.

Front

What is the average rate of change of the function f(x) = 2x^2 - 3 from x=0 to x=2?

Back

Average rate of change = (f(2) - f(0)) / (2 - 0) = (5 - (-3)) / 2 = 4.

Front

What is the average rate of change of the function f(x) = 1/(x-1) over the interval [-5, -2]?

Back

Average rate of change = (f(-2) - f(-5)) / (-2 - (-5)) = (1/(-3) - 1/(-6)) / 3 = 1/18.

Front

What is a characteristic of a linear function?

Back

A linear function has a constant rate of change.