Question

if f(x) = 8x + 7, find $\frac{f(a + h)-f(a)}{h}$. the value of $\frac{f(a + h)-f(a)}{h}$ for f(x) = 8x + 7 is . (type an integer or a simplified fraction.)

Explanation:

Step1: Find f(a + h)

Substitute x = a + h into f(x):
$f(a + h)=8(a + h)+7=8a+8h + 7$

Step2: Find f(a)

Substitute x = a into f(x):
$f(a)=8a + 7$

Step3: Calculate f(a + h) - f(a)

$(8a+8h + 7)-(8a + 7)=8a+8h + 7-8a - 7=8h$

Step4: Calculate $\frac{f(a + h)-f(a)}{h}$

$\frac{8h}{h}=8$

Answer:

8