1.3 Rate of Change and Initial Value

Front

What is the average rate of change?

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

How do you calculate the average rate of change over an interval [a,b]?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a)

Front

What is the initial value in a linear function?

Back

The initial value is the value of the function when the input is zero, often represented as the y-intercept in a linear equation.

Front

What does a positive rate of change indicate?

Back

A positive rate of change indicates that the function is increasing over the interval.

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that the function is decreasing over the interval.

Front

What is the rate of change of the function f(x) = x^3 - 1 over the interval [-1,1]?

Back

1

Front

What is the rate of change of the function f(x) = x^2 - 6 over the interval [-4,4]?

Back

0

Front

What is the average rate of change of the function f(x) = 2x - 3 over the interval [-4,4]?

Back

2

Front

If a function has a constant rate of change, what type of function is it?

Back

It is a linear function.

Front

What is the formula for the slope of a line?

Back

Slope (m) = (y2 - y1) / (x2 - x1)