Question

Find the difference quotient,

f(x+h)-f(x)/h ,
for the function and simplify it.

f(x) = 8x - 13

Answer 1

The difference quotient for the function f(x) = 8x - 13 is 8, which is found by substituting x + h into the function, subtracting f(x), and dividing by h.

Step-by-step explanation:

To find the difference quotient for the function f(x) = 8x - 13, we can plug in x+h into the function to get f(x+h) and then subtract f(x) from it, and finally divide the result by h.

First, let's find f(x+h):

• f(x+h) = 8(x+h) - 13
• f(x+h) = 8x + 8h - 13

Now, let's compute the difference quotient:

• \(\frac{f(x+h)-f(x)}{h} = \frac{(8x + 8h - 13) - (8x - 13)}{h}\)
• \(\frac{f(x+h)-f(x)}{h} = \frac{8x + 8h - 13 - 8x + 13}{h}\)
• \(\frac{f(x+h)-f(x)}{h} = \frac{8h}{h}\)
• \(\frac{f(x+h)-f(x)}{h} = 8\)

The 8x and -13 terms cancel out, leaving us with only terms that include h. After simplifying, the h's also cancel out, leaving us with the simplified difference quotient of 8.