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We are given the function \( f(x) = 5x - 5 \) and we need to evaluate the following expressions:

1. \( f(a) \)
2. \( f(a+h) \)
3. \( \frac{f(a+h) - f(a)}{h} \)

Let's calculate these step by step.

### 1. \( f(a) \)
Substitute \( a \) into the function \( f(x) = 5x - 5 \):

\[
f(a) = 5a - 5
\]

### 2. \( f(a+h) \)
Substitute \( a+h \) into the function:

\[
f(a+h) = 5(a+h) - 5 = 5a + 5h - 5
\]

### 3. \( \frac{f(a+h) - f(a)}{h} \)
Now, subtract \( f(a) \) from \( f(a+h) \):

\[
f(a+h) - f(a) = (5a + 5h - 5) - (5a - 5) = 5h
\]

Finally, divide by \( h \):

\[
\frac{f(a+h) - f(a)}{h} = \frac{5h}{h} = 5
\]

### Final Answers:
1. \( f(a) = 5a - 5 \)
2. \( f(a+h) = 5a + 5h - 5 \)
3. \( \frac{f(a+h) - f(a)}{h} = 5 \)

Would you like more details or have any other questions? Here are five additional related questions:

1. How would the derivative of \( f(x) = 5x - 5 \) be interpreted geometrically?
2. What happens to the difference quotient as \( h \to 0 \)?
3. How does the constant term \( -5 \) affect the slope of the function?
4. Can you find the second derivative of \( f(x) \)?
5. How would this process change if \( f(x) \) were a quadratic function?

**Tip:** The difference quotient \( \frac{f(a+h) - f(a)}{h} \) is fundamental in understanding the derivative, which represents the slope of the function at any point.

Given the function f(x) = 5x - 5, evaluate and simplify the expressions: f(a), f(a + h), and (f(a + h) - f(a)) / h.

Learn how to simplify expressions for the linear function f(x) = 5x - 5, including f(a), f(a + h), and the difference quotient. This problem covers key algebraic concepts related to functions and is suitable for high school students.

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