Graph Transformations: Shifting Functions

JC·

Math

Preview

At a Glance

Grade Level12th Grade

SubjectMath

Original Prompt

can you give me a detailed lesson on these objectives, Translate the graph of a function using y=k + f (x-h) and Write and simplify the translated equation of a function having DO NOW with interactive or guide questions and examples, ACTIVITY/EXPLORE with guide questions and worksheet with answer key, QUICK NOTES, GUIDED PRACTICE have a interactive questions so that students are really engage and guided with answer key, INDEPENDENT PRACTICE with answer key , CHECK YOUR UNDERSTANDING with answer

This lesson focuses on the concept of graph transformations, specifically how to shift functions, through the formula y = k + f(x-h). Students will learn how to identify the horizontal and vertical shifts of a function based on changes in the parameters h and k. The lesson begins with the parent function f(x) = x², prompting students to analyze transformations such as g(x) = x² + 3 (a vertical shift) and h(x) = (x-2)² (a horizontal shift). Key vocabulary such as 'Parent Function', 'Vertical Shift', and 'Horizontal Shift' is introduced, along with examples of how these transformations affect the graph's position. Students will practice identifying shifts using various transformed equations and will have opportunities for guided and independent practice to solidify their understanding of translating functions, writing new equations, and sketching graphs accordingly.