Graphing Functions with a Given Domain

Algebra 2 Grades High School 8:38 Video
Print Lesson Plan Watch Video

Lesson Description

This lesson focuses on graphing functions when provided with a specific domain. Students will learn how to substitute domain values into a function to determine corresponding range values, and then graph these points. The lesson emphasizes understanding the impact of absolute value and quadratic functions on the shape of the graph.

Video Resource

Graph Given Domain Algebra

Kevinmathscience

Duration: 8:38
Watch on YouTube

Key Concepts

  • Domain and Range
  • Function Evaluation
  • Graphing Functions
  • Absolute Value Functions
  • Quadratic Functions

Learning Objectives

  • Students will be able to evaluate a function for a given domain and determine the corresponding range.
  • Students will be able to graph the points generated from the domain and range to represent the function.
  • Students will be able to recognize the impact of absolute value on the shape of a graph and the impact of a quadratic equation on the shape of a graph.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concepts of domain and range. Briefly discuss how the domain represents the input values (x-values) and the range represents the output values (y-values). Show the video.
  • Video Analysis and Guided Practice (15 mins)
    Pause the video at various points to explain the steps being taken. Emphasize the importance of substituting each value from the domain into the function. Work through the first example in the video together, step-by-step, on the board or screen. Address any questions as they arise.
  • Independent Practice (15 mins)
    Provide students with additional functions and domains to graph. Encourage them to work independently or in pairs. Circulate the classroom to provide assistance and answer questions. Use functions similar to those in the video, gradually increasing in complexity.
  • Discussion and Review (10 mins)
    Bring the class back together to discuss the practice problems. Have students share their solutions and explain their reasoning. Review the key concepts and address any remaining questions. Discuss how the different types of functions affect the shape of the graphs (e.g., linear, absolute value, quadratic).

Interactive Exercises

  • Desmos Activity
    Have students use Desmos to graph various functions with defined domains. They can explore how changing the domain affects the graph. This could be a pre-built Desmos activity or a worksheet with specific instructions.

Discussion Questions

  • What is the difference between domain and range?
  • How does the absolute value affect the graph of a function?
  • How do you know if you need to connect the dots when graphing?
  • What are some real-world examples of functions with limited domains?

Skills Developed

  • Function Evaluation
  • Graphing Skills
  • Problem-Solving
  • Analytical Thinking

Multiple Choice Questions

Question 1:

What is the domain of a function?

Correct Answer: The set of all input values (x-values).

Question 2:

If f(x) = |x - 2| and the domain is {0, 1, 2, 3}, what is the range?

Correct Answer: {0, 1}

Question 3:

What shape does the graph of an absolute value function typically have?

Correct Answer: A V shape.

Question 4:

What is the first step in graphing a function given a specific domain?

Correct Answer: Substitute each value from the domain into the function.

Question 5:

If f(x) = x^2 - 1 and the domain is {-2, -1, 0, 1, 2}, what is the value of f(0)?

Correct Answer: -1

Question 6:

Which of the following represents the output of a function?

Correct Answer: y-value

Question 7:

What is the result of substituting x = -3 into the function f(x) = |x| + 2?

Correct Answer: 5

Question 8:

What do you call the point where a function reaches its minimum or maximum value?

Correct Answer: Vertex

Question 9:

Which of the following best describes the graph of f(x) = x^2?

Correct Answer: Parabola

Question 10:

If the domain is only whole numbers, should you connect the dots on your graph?

Correct Answer: No

Fill in the Blank Questions

Question 1:

The set of all possible input values for a function is called the ______.

Correct Answer: domain

Question 2:

The set of all possible output values for a function is called the ______.

Correct Answer: range

Question 3:

To find the range of a function for a given domain, you must ______ each value of the domain into the function.

Correct Answer: substitute

Question 4:

The graph of f(x) = |x| has a _______ shape.

Correct Answer: v

Question 5:

The highest or lowest point on a parabola is called the ______.

Correct Answer: vertex

Question 6:

When a domain is restricted, we only plot the points that are ______ of that domain.

Correct Answer: part

Question 7:

When a domain consists of discrete points, it's important not to ______ the plotted points.

Correct Answer: connect

Question 8:

The function f(x) = x^2 is a ______ function.

Correct Answer: quadratic

Question 9:

In the function notation f(x), 'x' represents the ______ variable.

Correct Answer: input

Question 10:

The absolute value of a number is always ______ or positive.

Correct Answer: zero

Educational Standards

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. 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.

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