Final answer:
Therefore, the difference quotient of the function f(x) = -8x - 35 is -8. The difference quotient of the function f(x) = -8x - 35 is -8.
Step-by-step explanation:
The difference quotient of a function is a measure of the average rate of change of the function over a small interval. In the case of the function f(x) = -8x - 35, the difference quotient can be represented as:
[(f(x+h) - f(x)) / h]
Substituting the given function into the difference quotient expression, we get:
[(f(x+h) - f(x)) / h] = [(-8(x+h) - 35) - (-8x - 35)] / h
Simplifying further, we have:
[(f(x+h) - f(x)) / h] = [-8x - 8h - 35 + 8x + 35] / h
Combining like terms, we get:
[(f(x+h) - f(x)) / h] = [(-8h) / h]
Simplifying the expression, we obtain:
[(-8h) / h] = -8
Therefore, the difference quotient of the function f(x) = -8x - 35 is -8.