Analyze the effect on the graphs of f(x) = 1/x when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d Video Lesson

About This Video

Curriculum-aligned Grade 11 Mathematics lesson video for Analyze the effect on the graphs of f(x) = 1/x when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d. Use it for classroom preview, instruction support, or home review.

This watch page is dedicated to the video. For the complete text lesson plan, activities, standards alignment, and answer guides, use the companion lesson page: Analyze the effect on the graphs of f(x) = 1/x when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d lesson plan.

Video Learning Notes

In this lesson, students learned how the graph of the reciprocal function f(x) = 1/x changes when transformed by multiplying by a constant, replacing x by bx, and shifting horizontally and vertically. They explored how these transformations affect the graph's shape, position, and asymptotes. Students also practiced formulating and solving rational equations that model real-world situations, reinforcing their understanding of rational functions and their applications.

Learning Goals

• Analyze how multiplying f(x) = 1/x by a positive or negative constant a affects the graph's shape and orientation.
• Analyze how replacing x by bx in f(x) = 1/x, for positive or negative b, affects the graph's horizontal stretch or compression and reflection.
• Analyze how shifting the graph horizontally by c units, replacing x by (x - c), changes the graph's position.
• Analyze how shifting the graph vertically by d units, adding d to f(x), changes the graph's position.
• Formulate rational equations based on real-world contexts involving transformations of f(x) = 1/x.

Curriculum Context

Grade: Grade 11

Subject: Mathematics

Curriculum: TEKS