Questions: Finding a difference quotient for a linear or quadratic function Find the difference quotient (f(x+h)-f(x))/h, where h ≠ 0, for the function below. f(x)=-8x+4 Simplify your answer as much as possible. (f(x+h)-f(x))/h= П.

Finding a difference quotient for a linear or quadratic function

Find the difference quotient (f(x+h)-f(x))/h, where h ≠ 0, for the function below.
f(x)=-8x+4

Simplify your answer as much as possible.
(f(x+h)-f(x))/h= П.

Transcript text: Finding a difference quotient for a linear or quadratic function Find the difference quotient $\frac{f(x+h)-f(x)}{h}$, where $h \neq 0$, for the function below. \[ f(x)=-8 x+4 \] Simplify your answer as much as possible. \[ \frac{f(x+h)-f(x)}{h}=\text { П. } \]

Solution

Solution Steps

Step 1: Define the Function

We are given the function $ f(x) = -8x + 4 $.

Step 2: Calculate $ f(x+h) $

To find the difference quotient, we first need to calculate $ f(x+h) $: \[ f(x+h) = -8(x+h) + 4 = -8x - 8h + 4 \]

Step 3: Calculate the Difference Quotient

Now, we can compute the difference quotient: \[ \frac{f(x+h) - f(x)}{h} = \frac{(-8x - 8h + 4) - (-8x + 4)}{h} \] Simplifying the expression: \[ = \frac{-8x - 8h + 4 + 8x - 4}{h} = \frac{-8h}{h} \] Since $ h \neq 0 $, we can simplify further: \[ = -8 \]

Final Answer

The difference quotient is \[ \boxed{-8} \]

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