## Correlation to Michigan Algebra 1 Standards

Section 20 Rational Functions

**Lesson: Introduction to Rational Function**

A1.2.2 Associate a given equation with a function whose zeros are the solutions of the equation.

**A1.1.2** Know the properties of exponents and roots and apply them in algebraic expressions.

**A1.1.3** Factor algebraic expressions using, for example, greatest common factor, grouping, and the special product identities.

**A2.1.3** Represent functions in symbols, graphs, tables, diagrams, or words and translate among representations.

**A2.1.6** Identify the zeros of a function, the intervals where the values of a function are positive or negative, and describe
the behavior of a function as x approaches positive or negative infinity, given the symbolic and graphical representations.

**A2.1.7** Identify and interpret the key features of a function from its graph or its formula(s).

**A2.3.1** Identify a function as a member of a family of functions based on its symbolic or graphical representation. Recognize
that different families of functions have different asymptotic behavior.

**Lesson: Simplifying Rational Exponents**

Major Emphasis:

A1.1.2 Know the properties of exponents and roots and apply them in algebraic expressions.

**A1.1.3** Factor algebraic expressions using, for example, greatest common factor, grouping, and the special product identities.

**Lesson: Solving Rational Functions**

Major Emphasis:

A1.2.2 Associate a given equation with a function whose zeros are the solutions of the equation.

**A1.1.2** Know the properties of exponents and roots and apply them in algebraic expressions.

**A1.1.3** Factor algebraic expressions using, for example, greatest common factor, grouping, and the special product identities.

**Lesson: Holes, Asymptotes and Graphs**

Major Emphasis:

A2.1.7 Identify and interpret the key features of a function from its graph or its formula(s).

**A2.1.6** Identify the zeros of a function, the intervals where the values of a function are positive or negative, and describe the
behavior of a function as x approaches positive or negative infinity, given the symbolic and graphical representations.

**A2.3.1** Identify a function as a member of a family of functions based on its symbolic or graphical representation. Recognize that
different families of functions have different asymptotic behavior.

**Lesson: Horizontal Asymptotes**

Major Emphasis:

A2.1.7 Identify and interpret the key features of a function from its graph or its formula(s).

**A2.1.6** Identify the zeros of a function, the intervals where the values of a function are positive or negative, and describe the
behavior of a function as x approaches positive or negative infinity, given the symbolic and graphical representations.

**A2.3.1** Identify a function as a member of a family of functions based on its symbolic or graphical representation. Recognize that
different families of functions have different asymptotic behavior.