Question

attempt 1: 10 attempts remaining. given the function $f(x) = 7x - 6$, calculate the following values: $f(a) = $, $f(a + h) = $, $\frac{f(a + h) - f(a)}{h} = $, submit answer, next item

Explanation:

Step1: Calculate \( f(a) \)

Substitute \( x = a \) into \( f(x) = 7x - 6 \).
\( f(a) = 7a - 6 \)

Step2: Calculate \( f(a + h) \)

Substitute \( x = a + h \) into \( f(x) = 7x - 6 \).
\( f(a + h) = 7(a + h) - 6 = 7a + 7h - 6 \)

Step3: Calculate \( \frac{f(a + h) - f(a)}{h} \)

Substitute \( f(a + h) = 7a + 7h - 6 \) and \( f(a) = 7a - 6 \) into the formula.
\[

$$\begin{align*} \frac{f(a + h) - f(a)}{h} &= \frac{(7a + 7h - 6) - (7a - 6)}{h}\\ &= \frac{7a + 7h - 6 - 7a + 6}{h}\\ &= \frac{7h}{h}\\ &= 7 \end{align*}$$

\]

Answer:

s:

• \( f(a) = 7a - 6 \)
• \( f(a + h) = 7a + 7h - 6 \)
• \( \frac{f(a + h) - f(a)}{h} = 7 \)