Question

1) f(x) = 2x - 5
Determine the difference quotient

Answer 1

Answer:

Difference quotient: $\frac{f(x+h)-f(x)}{h}$ = 2

Step-by-step explanation:

The difference quotient is the word that we use when trying to calculate the average rate of change of the function over a specific interval, which in this case, is h.

The formula for calculating the difference quotient is:

• $\frac{f(x+h)-f(x)}{h}$

In order to determine the difference quotient of the function $f(x)=2x-5$ we need to first evaluate $f(x+h)$ of this function.

We can do so by substituting x + h for x into the function.

• $f(x+h)=2(x+h)-5$

Distribute 2 inside the parentheses.

• $f(x+h)=2x+2h-5$

Now that we have found f(x + h), we can use the formula for the difference quotient and substitute f(x + h) and f(x) into it:

• $\frac{(2x+2h-5)-(2x-5)}{h}$

Distribute the negative sign inside the parentheses.

• $\frac{2x+2h-5-2x+5}{h}$

Combine like terms in the numerator. The 2x and 5's cancel out. We are left with:

• $\frac{2h}{h}$

The h's cancel out, and this simplifies to:

• $2$

The difference quotient of f(x) is 2.