Net Change in Functions

The video tutorial explains the concept of net change in functions, which is the difference in the output values of a function as the input changes from one point to another. It provides two examples using the function f(x) = x^2 to demonstrate how to calculate net change. The first example calculates the net change from 1 to 3, resulting in a net change of 8. The second example calculates the net change from -2 to 2, resulting in a net change of 0, illustrating that the function returns to the same value at the end of the interval.

What is the net change of a function?

• The sum of outputs at two inputs

• The ratio of outputs at two inputs

• The difference between outputs at two inputs

• The product of outputs at two inputs

How is the net change calculated for a function f(x) as the input changes from A to B?

• f(A) + f(B)

• f(A) - f(B)

• f(A) * f(B)

• f(B) - f(A)

In the context of net change, what does f(B) - f(A) represent?

• The net change in the function's value

• The final value of the function

• The initial value of the function

• The average value of the function

For the function f(x) = x^2, what is the net change from x = 1 to x = 3?

• 10

• 4

• 6

• 8

What is the value of f(3) for the function f(x) = x^2?

• 6

• 9

• 12

• 15

What is the value of f(1) for the function f(x) = x^2?

• 3

• 2

• 1

• 0

In the example of f(x) = x^2, what does the net change from 1 to 3 tell us?

• The function decreases by 4

• The function decreases by 8

• The function increases by 8

• The function remains constant

For the function f(x) = x^2, what is the net change from x = -2 to x = 2?

• 2

• 0

• 8

• 4

What is the value of f(2) for the function f(x) = x^2?

• 2

• 4

• 6

• 8

What is the value of f(-2) for the function f(x) = x^2?

• 4

• 8

• 2

• 6