This worksheet provides twelve practice problems for performing basic operations like addition and subtraction on polynomial functions.

1. f(x) = 3x - 1, g(x) = x² + 2
(f + g)(x) = 3x - 1 + x² + 2 = x² + 3x + 1
(f - g)(x) = 3x - 1 - (x² + 2) = -x² + 3x - 3
(f · g)(x) = (3x - 1)(x² + 2) = 3x³ + 6x - x² - 2 = 3x³ - x² + 6x - 2
(f/g)(x) = (3x - 1)/(x² + 2), domain: all real numbers

2. f(x) = 2x² - 4x + 3, g(x) = x - 2
(f + g)(x) = 2x² - 4x + 3 + x - 2 = 2x² - 3x + 1
(f - g)(x) = 2x² - 4x + 3 - (x - 2) = 2x² - 5x + 5
(f · g)(x) = (2x² - 4x + 3)(x - 2) = 2x³ - 4x² - 4x² + 8x + 3x - 6 = 2x³ - 8x² + 11x - 6
(f/g)(x) = (2x² - 4x + 3)/(x - 2), domain: x ≠ 2

3. f(x) = x - 2, g(x) = x² - 4
(f + g)(x) = x - 2 + x² - 4 = x² + x - 6
(f - g)(x) = x - 2 - (x² - 4) = -x² + x + 2
(f · g)(x) = (x - 2)(x² - 4) = x³ - 4x - 2x² + 8 = x³ - 2x² - 4x + 8
(f/g)(x) = (x - 2)/(x² - 4) = (x - 2)/[(x - 2)(x + 2)] = 1/(x + 2), domain: x ≠ ±2

4. f(x) = 2x + 3, g(x) = 3x - 1
(f + g)(x) = 2x + 3 + 3x - 1 = 5x + 2
(f - g)(x) = 2x + 3 - (3x - 1) = -x + 4
(f · g)(x) = (2x + 3)(3x - 1) = 6x² - 2x + 9x - 3 = 6x² + 7x - 3
(f/g)(x) = (2x + 3)/(3x - 1), domain: x ≠ 1/3

5. f(x) = x² - 2x, g(x) = x + 1
(f + g)(x) = x² - 2x + x + 1 = x² - x + 1
(f - g)(x) = x² - 2x - (x + 1) = x² - 3x - 1
(f · g)(x) = (x² - 2x)(x + 1) = x³ + x² - 2x² - 2x = x³ - x² - 2x
(f/g)(x) = (x² - 2x)/(x + 1), domain: x ≠ -1

6. f(x) = 2x - 1, g(x) = x² - 3
(f + g)(x) = 2x - 1 + x² - 3 = x² + 2x - 4
(f - g)(x) = 2x - 1 - (x² - 3) = -x² + 2x + 2
(f · g)(x) = (2x - 1)(x² - 3) = 2x³ - 6x - x² + 3 = 2x³ - x² - 6x + 3
(f/g)(x) = (2x - 1)/(x² - 3), domain: x ≠ ±√3

7. f(x) = x² - 2x - 3, g(x) = x + 1
(f + g)(x) = x² - 2x - 3 + x + 1 = x² - x - 2
(f - g)(x) = x² - 2x - 3 - (x + 1) = x² - 3x - 4
(f · g)(x) = (x² - 2x - 3)(x + 1) = x³ + x² - 2x² - 2x - 3x - 3 = x³ - x² - 5x - 3
(f/g)(x) = (x² - 2x - 3)/(x + 1) = [(x - 3)(x + 1)]/(x + 1) = x - 3, domain: x ≠ -1

8. f(x) = 3x - 2, g(x) = 2x + 1
(f + g)(x) = 3x - 2 + 2x + 1 = 5x - 1
(f - g)(x) = 3x - 2 - (2x + 1) = x - 3
(f · g)(x) = (3x - 2)(2x + 1) = 6x² + 3x - 4x - 2 = 6x² - x - 2
(f/g)(x) = (3x - 2)/(2x + 1), domain: x ≠ -1/2

9. f(x) = x - 3, g(x) = x² - 9
(f + g)(x) = x - 3 + x² - 9 = x² + x - 12
(f - g)(x) = x - 3 - (x² - 9) = -x² + x + 6
(f · g)(x) = (x - 3)(x² - 9) = x³ - 9x - 3x² + 27 = x³ - 3x² - 9x + 27
(f/g)(x) = (x - 3)/(x² - 9) = (x - 3)/[(x - 3)(x + 3)] = 1/(x + 3), domain: x ≠ ±3

10. f(x) = 4x - 1, g(x) = 2x - 3
(f + g)(x) = 4x - 1 + 2x - 3 = 6x - 4
(f - g)(x) = 4x - 1 - (2x - 3) = 2x + 2
(f · g)(x) = (4x - 1)(2x - 3) = 8x² - 12x - 2x + 3 = 8x² - 14x + 3
(f/g)(x) = (4x - 1)/(2x - 3), domain: x ≠ 3/2

11. f(x) = x² - 4, g(x) = x - 2
(f + g)(x) = x² - 4 + x - 2 = x² + x - 6
(f - g)(x) = x² - 4 - (x - 2) = x² - x - 2
(f · g)(x) = (x² - 4)(x - 2) = x³ - 2x² - 4x + 8
(f/g)(x) = (x² - 4)/(x - 2) = [(x - 2)(x + 2)]/(x - 2) = x + 2, domain: x ≠ 2

12. f(x) = 5x + 2, g(x) = x² - 4
(f + g)(x) = 5x + 2 + x² - 4 = x² + 5x - 2
(f - g)(x) = 5x + 2 - (x² - 4) = -x² + 5x + 6
(f · g)(x) = (5x + 2)(x² - 4) = 5x³ - 20x + 2x² - 8 = 5x³ + 2x² - 20x - 8
(f/g)(x) = (5x + 2)/(x² - 4), domain: x ≠ ±2