The difference quotient for a function $f(x)$ is given by the formula:

$\frac{f(x+h) - f(x)}{h}$

where $h$ is a small increment in $x$.

For the function $f(x) = -2x + 5$, we will first find $f(x+h)$:

$f(x+h) = -2(x+h) + 5 = -2x - 2h + 5$

Now, substitute this into the difference quotient formula:

$\frac{f(x+h) - f(x)}{h} = \frac{(-2x - 2h + 5) - (-2x + 5)}{h}$

Simplify the expression:

= \frac{-2h}{h} = -2$$ Thus, the difference quotient for the function $$f(x) = -2x + 5$$ is $$-2$$. Would you like further details or have any questions? Here are 5 related questions: 1. What does the difference quotient represent geometrically? 2. How does the difference quotient relate to the derivative of a function? 3. What is the difference quotient for the function $$f(x) = x^2$$? 4. How does the difference quotient change for a quadratic function? 5. Can you interpret the result $$-2$$ in terms of the slope of a linear function? **Tip:** The difference quotient is a fundamental concept for finding the derivative, which measures the rate of change of a function.