Grade 12 Math: Rational Expressions, Equations, and Functions

This worksheet covers key concepts in rational expressions, equations, and functions for Grade 12 mathematics students.

Grade 12 Math AlgebraRational Expressions Equations and Functions

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Includes

Fill in the BlanksMultiple Choice3 Short AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSA.APR.D.6CCSS.MATH.CONTENT.HSA.APR.D.7CCSS.MATH.CONTENT.HSA.REI.A.2

Topics

AlgebraRational ExpressionsRational EquationsRational FunctionsGrade 12 Math

8 sections · Free to use · Printable

Rational Expressions, Equations, and Functions

Name:

Date:

Score:

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)?

x + 2

x - 2

x^2

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

x ≠ 0

x ≠ 3

All real numbers

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.

True

False

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.

True

False

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.