Question

review for exam 1 over chapters 2 and 3
score: 20/32 answered: 22/32
question 23
for the function ( f(x)=-3x + 7 ), evaluate and simplify the difference quotient.

Explanation:

Step1: Recall the formula for the difference quotient

The difference quotient formula is \(\frac{f(x + h)-f(x)}{h}\).

Step2: Find \(f(x + h)\)

Given \(f(x)=-3x + 7\), then \(f(x + h)=-3(x + h)+7=-3x-3h + 7\).

Step3: Substitute \(f(x + h)\) and \(f(x)\) into the difference quotient formula

$$
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$$

Step4: Simplify the numerator and then the fraction

The numerator \(-3x-3h + 7 + 3x-7=-3h\). So \(\frac{-3h}{h}=-3\).

Answer:

\(-3\)