Rational Expressions, Equations, and Functions
A Grade 10 math worksheet covering simplification, operations, solving equations, and analyzing rational functions.
Includes
Standards
Topics
Rational Expressions, Equations, and Functions
Name:
Date:
Score:
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. State any restrictions on the variable.
$$\frac{x^2 - 4x - 12}{x^2 - 4}$$
2. Perform the indicated operation and simplify. State any restrictions on the variable.
$$\frac{3y}{y^2 - 25} \div \frac{9y^2}{2y - 10}$$
3. Solve the following rational equation. Identify any extraneous solutions.
$$\frac{2}{x+1} + \frac{1}{x-1} = \frac{4}{x^2-1}$$
The least common denominator (LCD) is .
Multiplying by the LCD, the equation becomes .
The solution(s) to the equation are x = .
The extraneous solution(s), if any, are x = .
4. What is the domain of the rational function $$f(x) = \frac{x-3}{x^2 - x - 6}$$?
$$x \neq 3$$
$$x \neq -2$$
$$x \neq 3, x \neq -2$$
$$x \neq 3, x \neq 2$$
5. Consider the function $$g(x) = \frac{x+2}{x-1}$$.
a) State the equation of the vertical asymptote:
b) State the equation of the horizontal asymptote:
c) State the x-intercept(s):
d) State the y-intercept(s):
e) Sketch the graph of the function on the coordinate plane below, clearly labeling any asymptotes and intercepts.