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Let's break down the problem and solve it step by step.

We are given two functions:

\[
r(x) = 5x
\]
\[
s(x) = 2x - 4
\]

### 1. Write the expression for \((s + r)(x)\):
\[
(s + r)(x) = s(x) + r(x)
\]

Substitute the given functions:

\[
(s + r)(x) = (2x - 4) + 5x = 7x - 4
\]

### 2. Write the expression for \((s \cdot r)(x)\):
\[
(s \cdot r)(x) = s(x) \cdot r(x)
\]

Substitute the given functions:

\[
(s \cdot r)(x) = (2x - 4) \cdot (5x)
\]

Now expand the product:

\[
(s \cdot r)(x) = 10x^2 - 20x
\]

### 3. Evaluate \((s - r)(x)\) for \(x = -2\):
\[
(s - r)(x) = s(x) - r(x)
\]

Substitute the given functions:

\[
(s - r)(x) = (2x - 4) - 5x = 2x - 4 - 5x = -3x - 4
\]

Now evaluate this for \(x = -2\):

\[
(s - r)(-2) = -3(-2) - 4 = 6 - 4 = 2
\]

### Final Answers:
1. \((s + r)(x) = 7x - 4\)
2. \((s \cdot r)(x) = 10x^2 - 20x\)
3. \((s - r)(-2) = 2\)

Would you like further clarification on any step?

### Follow-up Questions:
1. How do we find \((s \div r)(x)\)?
2. What is the value of \((s \cdot r)(-2)\)?
3. How do you graph \((s + r)(x)\)?
4. What are the roots of the function \((s - r)(x) = 0\)?
5. Can you explain how to factor \((s \cdot r)(x)\)?

### Tip:
When adding or subtracting functions, always combine like terms carefully, and when multiplying, use the distributive property (or FOIL for binomials) to expand the expression properly.

Suppose that the functions r and s are defined for all real numbers x as follows: r(x) = 5x and s(x) = 2x - 4. Write the expressions for (s + r)(x) and (s · r)(x) and evaluate (s - r)(-2).

Learn how to perform operations with functions, such as addition, subtraction, and multiplication, using the functions r(x) = 5x and s(x) = 2x - 4. This includes step-by-step solutions for finding (s + r)(x), (s · r)(x), and evaluating (s - r)(-2). Suitable for students in Grades 9-10.

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