Find the difference of functions s and r shown below.

r(x) = –x² + 3x            s(x) = 2x + 1

(s – r)(x)

To find the difference of the functions \( s(x) \) and \( r(x) \), we subtract \( r(x) \) from \( s(x) \):

\[
(s - r)(x) = s(x) - r(x)
\]

Given that:

\[
r(x) = -x^2 + 3x \quad \text{and} \quad s(x) = 2x + 1
\]

Substituting the expressions for \( s(x) \) and \( r(x) \):

\[
(s - r)(x) = (2x + 1) - (-x^2 + 3x)
\]

Simplifying the expression:

\[
(s - r)(x) = 2x + 1 + x^2 - 3x
\]

Now, combine like terms:

\[
(s - r)(x) = x^2 - x + 1
\]

So, the difference of the functions is:

\[
(s - r)(x) = x^2 - x + 1
\]

Would you like any further details or explanations?

Here are some related questions:
1. What is the sum of the functions \( s(x) \) and \( r(x) \)?
2. How would you find the product of \( s(x) \) and \( r(x) \)?
3. What is the derivative of \( (s - r)(x) \)?
4. How would you solve \( (s - r)(x) = 0 \)?
5. What are the domain and range of \( (s - r)(x) \)?

**Tip:** Always combine like terms when subtracting or adding polynomial functions to simplify the expression.

Find the difference of functions s and r shown below.
r(x) = –x² + 3x
s(x) = 2x + 1
(s – r)(x)

Discover how to find the difference between two functions, r(x) = –x² + 3x and s(x) = 2x + 1. This solution breaks down key algebraic concepts, including function subtraction and polynomial simplification. Suitable for high school students in Grades 9-11.

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