Grade 12 Math: Rational Expressions, Equations, and Functions

Rational Expressions, Equations, and Functions

Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. A rational expression is a fraction where the numerator and denominator are both  .

2. When simplifying rational expressions, we must identify values that make the denominator equal to  .

3. An   asymptote occurs when the degree of the numerator is less than the degree of the denominator.

1. Which of the following is equivalent to (x^2 - 4) / (x - 2)?

2. What is the domain of the function f(x) = 1 / (x - 3)?

1. Simplify the following rational expression: (x^2 + 5x + 6) / (x + 2)

2. Simplify the following rational expression: (3x^2 - 9x) / (x - 3)

1. Solve the equation: 2 / (x + 1) = 4 / (x - 1)

2. Solve the equation: (x + 2) / (x - 3) = (x - 1) / (x + 4)

1. A vertical asymptote occurs where the denominator of a rational function is zero and the numerator is non-zero.

2. A hole in the graph of a rational function occurs when a factor in the numerator cancels with an identical factor in the denominator.

1. For the function f(x) = (x + 1) / (x - 2), identify the vertical and horizontal asymptotes.

2. Sketch the graph of f(x) = 1 / x on the coordinate plane below, labeling any asymptotes.