Transform Your Understanding: Graphing Absolute Value Functions

Algebra 2 Grades High School 6:55 Video
Print Lesson Plan Watch Video

Lesson Description

Explore the world of absolute value functions and master graphing techniques using transformations. Learn to shift, stretch, and reflect these V-shaped graphs with ease!

Video Resource

Graphing Absolute Value Functions with Transformations

Mario's Math Tutoring

Duration: 6:55
Watch on YouTube

Key Concepts

  • Parent function of absolute value: y = |x|
  • Transformations: vertical shifts, horizontal shifts, vertical stretches/compressions, reflections
  • Vertex form of absolute value function: y = a|x - h| + k

Learning Objectives

  • Students will be able to identify and graph the parent absolute value function.
  • Students will be able to identify and apply transformations to graph absolute value functions in the form y = a|x - h| + k.
  • Students will be able to determine the domain and range of absolute value functions.

Educator Instructions

  • Introduction (5 mins)
    Briefly review the concept of absolute value and its effect on numbers. Introduce the parent absolute value function y = |x| and its V-shape graph. Mention the importance of understanding transformations in graphing.
  • Video Presentation (15 mins)
    Play the Mario's Math Tutoring video 'Graphing Absolute Value Functions with Transformations'. Encourage students to take notes on key concepts like the vertex form of the equation and how each parameter (a, h, k) affects the graph.
  • Guided Practice (15 mins)
    Work through example problems similar to those in the video, step-by-step. Focus on identifying the transformations (horizontal shift, vertical shift, stretch/compression, reflection) from the equation and then using that information to graph the function. Emphasize finding the vertex first.
  • Independent Practice (10 mins)
    Provide students with a worksheet or online exercises with absolute value function equations. Ask them to graph these functions, identifying the transformations and the vertex. Circulate to provide assistance as needed.
  • Wrap-up & Assessment (5 mins)
    Briefly review the key concepts. Administer a short multiple choice quiz to assess understanding. Preview the next lesson on more complex function transformations.

Interactive Exercises

  • Graphing App Exploration
    Use a graphing calculator or online graphing tool (like Desmos or GeoGebra) to explore how changing the parameters (a, h, k) in the equation y = a|x - h| + k affects the graph of the absolute value function in real-time. Students can experiment and make observations.
  • Matching Game
    Create a matching game where students match absolute value function equations with their corresponding graphs. This can be done using physical cards or a digital platform.

Discussion Questions

  • How does the value of 'a' in y = a|x - h| + k affect the graph of the absolute value function?
  • Explain the difference between a vertical stretch and a vertical compression. How do they affect the graph's appearance?
  • How do you determine the vertex of an absolute value function given its equation in vertex form?
  • What are the domain and range of a standard absolute value function, and how can transformations affect them?
  • If a graph is reflected across the x-axis, what transformation is represented in the equation?

Skills Developed

  • Graphing absolute value functions
  • Identifying and applying transformations
  • Analyzing equations to predict graphical behavior
  • Problem-solving
  • Critical thinking

Multiple Choice Questions

Question 1:

What is the vertex of the absolute value function y = |x + 3| - 2?

Correct Answer: (-3, -2)

Question 2:

Which transformation does the '-4' represent in the function y = |x| - 4?

Correct Answer: Vertical shift down 4 units

Question 3:

What effect does a negative 'a' value have on the graph of y = a|x - h| + k?

Correct Answer: Reflection across the x-axis

Question 4:

Which of the following equations represents a vertical stretch of the parent function y = |x|?

Correct Answer: y = 3|x|

Question 5:

What is the domain of the function y = 2|x - 1| + 3?

Correct Answer: All real numbers

Question 6:

What is the range of the function y = -|x + 2| + 5?

Correct Answer: y ≤ 5

Question 7:

Which equation would result in a wider graph than the parent function y = |x|?

Correct Answer: y = 0.25|x|

Question 8:

What does the 'h' represent in the vertex form of the equation y = a|x - h| + k?

Correct Answer: Horizontal shift

Question 9:

If a vertex is at (2, -1) what are the transformations made to the parent function y = |x|?

Correct Answer: Shifted right 2, shifted down 1

Question 10:

Which function has a vertex that is located in quadrant III?

Correct Answer: y = -|x + 2| - 3

Fill in the Blank Questions

Question 1:

The parent function of an absolute value function is y = _______.

Correct Answer: |x|

Question 2:

In the equation y = a|x - h| + k, the vertex of the absolute value function is located at (______, ______).

Correct Answer: h, k

Question 3:

A negative 'a' value in y = a|x - h| + k results in a ________ across the x-axis.

Correct Answer: reflection

Question 4:

The transformation represented by y = |x - 5| is a horizontal shift to the _______ by 5 units.

Correct Answer: right

Question 5:

If 'a' is greater than 1 in the equation y = a|x|, there will be a vertical _______.

Correct Answer: stretch

Question 6:

The __________ is the point where the absolute value graph changes direction.

Correct Answer: vertex

Question 7:

The domain of a typical absolute value function is __________.

Correct Answer: all real numbers

Question 8:

A vertical shift of down 3 units for the parent function would be represented as y = |x| ______.

Correct Answer: - 3

Question 9:

A value of 'a' between 0 and 1 such as y = 0.5|x|, is known as a vertical _________

Correct Answer: compression

Question 10:

In the equation y = a|x - h| + k, the 'h' represents a _______ shift.

Correct Answer: horizontal

Educational Standards

A2.F.1.2:Identify the parent forms of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [𝑓(𝑥 + 𝑐), 𝑓(𝑥) + 𝑐, 𝑓(𝑐𝑥), and 𝑐𝑓(𝑥)] algebraically and graphically. A2.F.1.1:Use algebraic, interval, and set notations to specify the domain and range of various types of functions, and evaluate a function at a given point in its domain.

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans