Simplify the difference quotient for the linear function $f(x)$, and use it to identify the rate of change of the function.
-$f(x)=75 x-675$
A) -675
B) 75
C) 675
D) -75

Question

Quizplus · Accepted Answer

The difference quotient for a linear function $f(x) = mx + b$ is given by $\frac{f(x+h)-f(x)}{h}$, where $h$ is a non-zero number. For the given function $f(x) = 75x - 675$, substituting into the difference quotient formula gives $\frac{(75(x+h)-675)-(75x-675)}{h} = \frac{75h}{h} = 75$. This simplifies to 75, which represents the slope of the line or the rate of change of the function.

Simplify the Difference Quotient for the Linear Function f(x)f(x)f(x) , and Use It to Identify the Rate of Change

Simplify the Difference Quotient for the Linear Function $f(x)$ , and Use It to Identify the Rate of Change