The phrase refers to a resource that provides solutions to problems involving the transformation of functions, specifically translations, within a section or unit designated as “1.12 a”. Translation, in this mathematical context, describes the shifting of a function’s graph horizontally or vertically on a coordinate plane. The ‘answer key’ component indicates a collection of correct solutions designed to verify the accuracy of calculations performed on these types of problems. As an example, a problem might involve translating the function f(x) = x2 two units to the right and one unit upwards, resulting in the translated function g(x) = (x – 2)2 + 1. The associated answer key would then provide this correct functional representation as the solution.
Access to such solution sets offers several benefits in a learning environment. Primarily, it facilitates self-assessment and independent study, allowing individuals to confirm their understanding of translation principles and techniques. This supports improved accuracy in applying the rules of function transformations and reduces reliance on direct instructor feedback for every problem. The use of answer keys in mathematics education has a long history, reflecting the need for students to independently evaluate their work and develop problem-solving confidence. Efficient feedback mechanisms, such as solution keys, have been demonstrated to enhance learning outcomes.
