This math unit ushers students through a progressive exploration of the domain of functions represented by various types of fractional expressions. It begins with simpler concepts like determining the domain of functions formed by fractions where the denominator is a linear or quadratic expression, emphasizing understanding whether denominators could hit zero or if roots are complex. The unit then escalates to handle square roots in the denominator, moving from linear roots to more complex quadratic roots, immediately instructing students to address non-negative conditions that ensure valid domains. Equipped with these foundational skills, students advance to scenarios where both numerators and denominators incorporate linear functions, quadratic functions, or square roots. Each type of fractional function challenges students to consider multiple domain constraints such as avoiding undefined expressions and non-negative square roots. By the culmination of the unit, students are proficient in graphically representing these domains on number lines. The skill set includes algebraic manipulation to identify domain boundaries and use of number lines to clearly illustrate valid ranges of inputs for diverse and increasingly complex rational functions.Skills you will learn include:
Topics are small, focused areas which build towards the greater unit's goals.