Unveiling the Secrets: Graphing Absolute Value Functions

Algebra 2 Grades High School 17:20 Video
Print Lesson Plan Watch Video

Lesson Description

This lesson delves into graphing absolute value functions, covering key concepts and transformations. Students will learn to identify vertex, axis of symmetry, and understand how changes to the function affect the graph's shape and position.

Video Resource

Graph Absolute Value Functions Algebra

Kevinmathscience

Duration: 17:20
Watch on YouTube

Key Concepts

  • Absolute value definition and properties
  • Vertex form of an absolute value function
  • Transformations: vertical and horizontal shifts, reflections

Learning Objectives

  • Students will be able to graph absolute value functions accurately.
  • Students will be able to identify the vertex and axis of symmetry of an absolute value function.
  • Students will be able to describe the transformations applied to the parent function y = |x|.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of absolute value and its properties. Briefly discuss the parent function y = |x| and its graph.
  • Video Viewing (15 mins)
    Watch the Kevinmathscience video on graphing absolute value functions. Encourage students to take notes on key steps and examples.
  • Guided Practice (20 mins)
    Work through several examples of graphing absolute value functions, emphasizing how to identify the vertex and apply transformations. Start with simpler examples and gradually increase complexity.
  • Independent Practice (15 mins)
    Assign students practice problems to graph absolute value functions on their own. Provide support as needed.
  • Wrap-up and Discussion (5 mins)
    Review the main points of the lesson and answer any remaining questions. Preview the next lesson on related topics.

Interactive Exercises

  • Graphing Challenge
    Use an online graphing tool to graph various absolute value functions and observe the effects of changing the parameters (e.g., a, h, k in y = a|x - h| + k).

Discussion Questions

  • How does the absolute value function differ from other types of functions you've studied?
  • How do transformations affect the graph of an absolute value function?
  • What are some real-world applications of absolute value functions?

Skills Developed

  • Graphing functions
  • Applying transformations
  • Problem-solving
  • Analytical 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 equation y = -|x| represent?

Correct Answer: Reflection over the x-axis

Question 3:

What is the axis of symmetry for the function y = |x + 5| - 1?

Correct Answer: x = -5

Question 4:

Which equation represents a vertical stretch of the absolute value function y = |x| by a factor of 3?

Correct Answer: y = 3|x|

Question 5:

What is the range of the function y = |x| + 4?

Correct Answer: y ≥ 4

Question 6:

The graph of y = |x - 2| is shifted 2 units to the right of which function?

Correct Answer: y = |x|

Question 7:

If a function is reflected over the x-axis, what part of the equation changes?

Correct Answer: y becomes -y

Question 8:

Which absolute value function has a vertex at (-1, 3)?

Correct Answer: y = |x + 1| + 3

Question 9:

What effect does adding a constant 'c' inside the absolute value (y = |x + c|) have on the graph?

Correct Answer: Horizontal shift

Question 10:

Which of these describes a vertical compression?

Correct Answer: 0 < a < 1

Fill in the Blank Questions

Question 1:

The vertex of the absolute value function y = a|x - h| + k is at the point (____, ____).

Correct Answer: h, k

Question 2:

A reflection over the x-axis changes the sign of the _____ values.

Correct Answer: y

Question 3:

The parent function for absolute value functions is y = ____.

Correct Answer: |x|

Question 4:

A horizontal shift to the left is represented by adding a constant to x ______ the absolute value symbols.

Correct Answer: inside

Question 5:

The axis of symmetry for an absolute value function always passes through the _______.

Correct Answer: vertex

Question 6:

If 'a' is negative in y = a|x|, the graph is reflected over the _____-axis.

Correct Answer: x

Question 7:

The ________ is the lowest or highest point on an absolute value graph.

Correct Answer: vertex

Question 8:

Adding a constant outside the absolute value symbols shifts the graph ________.

Correct Answer: vertically

Question 9:

In the function y = |x - 4|, the graph is shifted 4 units to the ________.

Correct Answer: right

Question 10:

The equation for the axis of symmetry is always x = _______, where h is the x-coordinate of the vertex.

Correct Answer: h

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