Rational Expressions, Equations, and Functions
A Grade 11 math worksheet covering simplification, operations, solving equations, and analyzing rational functions.
Includes
Standards
Topics
Rational Expressions, Equations, and Functions
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. Simplify the following rational expression, stating any restrictions on the variables:
(x² - 9) / (x² - x - 12)
2. Complete the multiplication: ( (2x + 4) / (x² - 4) ) * ( (x - 2) / (6x) ) =
3. Complete the division: ( (x² + 5x + 6) / (x² - 9) ) ÷ ( (x + 2) / (x - 3) ) =
4. What is the sum of (3 / (x + 1)) + (2 / (x - 1))?
(5x + 1) / (x² - 1)
(5x - 1) / (x² - 1)
(5x + 5) / (x² - 1)
(5x - 5) / (x² - 1)
5. Solve the following rational equation for x. Remember to check for extraneous solutions:
3 / (x + 2) = 2 / (x - 1)
6. The rational function f(x) = (x + 3) / (x - 2) has a vertical asymptote at x = 2.
True
False
7. The rational function g(x) = (2x² + 1) / (x² - 4) has a horizontal asymptote at y = 0.
True
False
8. For the function h(x) = (x - 1) / (x + 3), identify the x-intercept, y-intercept, vertical asymptote, and horizontal asymptote. Then sketch a graph of the function.
x-intercept:
y-intercept:
Vertical Asymptote:
Horizontal Asymptote: