Question

Which of the following expressions represents f(x + h) - f(x) for the function f(x) = x² - 4x, where h is a constant?

1. 2hx + h² - 8x + 4h
2. 2hx + h² - 4h
3. h
4. f(h)
5. h² - 4h
6. None of the above

Answer 1

The difference f(x + h) - f(x) for the function f(x) = x² - 4x is represented by the expression 2hx + h² - 4h, which is option 2 from the provided list.

Step-by-step explanation:

The student's question involves finding the expression for f(x + h) - f(x) when f(x) is given as x² - 4x and h is a constant. First, we need to compute f(x + h):

f(x + h) = (x + h)² - 4(x + h) = x² + 2hx + h² - 4x - 4h

Now, we subtract f(x) from f(x + h):

f(x + h) - f(x) = (x² + 2hx + h² - 4x - 4h) - (x² - 4x)

By simplifying this expression, we are left with:

2hx + h² - 4h

Therefore, the expression that represents f(x + h) - f(x) for the given function is 2hx + h² - 4h, which corresponds to option 2 in the list provided by the student.