Unlocking Radical Functions: Graphing, Domain, and Range

Algebra 2 Grades High School 17:39 Video
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Lesson Description

Explore the world of radical functions! This lesson covers graphing techniques, determining domain and range, and applying these concepts to real-world scenarios.

Video Resource

Graphing Radical Functions Domain and Range

Kevinmathscience

Duration: 17:39
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Key Concepts

  • Radical functions
  • Domain of a function
  • Range of a function
  • Graphing radical functions
  • Transformations of radical functions

Learning Objectives

  • Students will be able to graph radical functions.
  • Students will be able to determine the domain and range of radical functions algebraically and graphically.
  • Students will be able to apply transformations to radical functions and analyze the resulting changes in the graph, domain, and range.

Educator Instructions

  • Introduction (5 mins)
    Begin by briefly reviewing the concept of functions and their domains and ranges. Introduce the concept of radical functions as a specific type of function with unique characteristics. Show the video 'Graphing Radical Functions Domain and Range' by Kevinmathscience.
  • Graphing Radical Functions (15 mins)
    Discuss the basic shape of radical functions (square root and cube root). Explain how to graph these functions by plotting points and identifying key features. Emphasize the impact of the index of the radical on the shape of the graph.
  • Domain and Range of Radical Functions (15 mins)
    Define domain and range in the context of radical functions. Explain how to determine the domain of a square root function by setting the radicand greater than or equal to zero. Discuss the range of square root and cube root functions. Provide examples and work through them step-by-step.
  • Transformations of Radical Functions (15 mins)
    Explore how transformations (shifts, stretches, reflections) affect the graph, domain, and range of radical functions. Demonstrate how to identify transformations from the function's equation and how to apply them to the graph. Give examples of equations and associated graphs so that students can apply them.
  • Practice and Application (10 mins)
    Provide students with practice problems involving graphing radical functions, determining their domain and range, and applying transformations. Encourage them to work individually or in pairs. Circulate to provide assistance and answer questions.

Interactive Exercises

  • Graphing Challenge
    Students use graphing calculators or online graphing tools to graph various radical functions and identify their domain and range.
  • Domain and Range Match
    Students match radical functions with their corresponding domains and ranges expressed in interval notation.

Discussion Questions

  • How does the index of a radical function affect its graph?
  • What is the relationship between the domain of a square root function and its radicand?
  • How do transformations affect the domain and range of radical functions?

Skills Developed

  • Graphing functions
  • Determining domain and range
  • Algebraic manipulation
  • Problem-solving
  • Analytical thinking

Multiple Choice Questions

Question 1:

What is the domain of the function f(x) = √(x - 3)?

Correct Answer: x ≥ 3

Question 2:

What is the range of the function f(x) = √x + 2?

Correct Answer: y ≥ 2

Question 3:

Which of the following transformations will shift the graph of f(x) = √x to the right by 4 units?

Correct Answer: f(x) = √(x - 4)

Question 4:

The graph of a cube root function extends:

Correct Answer: Above and below the x-axis

Question 5:

What is the y-intercept of f(x) = √(x + 9)?

Correct Answer: 3

Question 6:

Which of the following functions has a domain of all real numbers?

Correct Answer: f(x) = ³√x

Question 7:

A reflection over the x-axis of f(x) = √x is represented by which function?

Correct Answer: f(x) = -√x

Question 8:

The function f(x) = 2√x represents a _______ of the parent function f(x) = √x.

Correct Answer: Vertical stretch

Question 9:

What is the range of f(x) = -√x?

Correct Answer: y ≤ 0

Question 10:

How would the graph of y = √x + 5 compare to the graph of y = √x?

Correct Answer: Shifted up 5 units

Fill in the Blank Questions

Question 1:

The domain of a square root function is restricted because you cannot take the square root of a ______ number.

Correct Answer: negative

Question 2:

The range of f(x) = √x is all real numbers greater than or equal to ______.

Correct Answer: 0

Question 3:

The transformation f(x) = √x - 2 shifts the graph of f(x) = √x down by _____ units.

Correct Answer: 2

Question 4:

The domain of a cube root function is ______.

Correct Answer: all real numbers

Question 5:

The starting point on a graph of a square root function is (h, k). 'h' represents a ______ shift.

Correct Answer: horizontal

Question 6:

The function f(x) = √(-x) is a reflection over the ______ axis.

Correct Answer: y

Question 7:

Multiplying a radical function by a number greater than 1 results in a ______ stretch.

Correct Answer: vertical

Question 8:

The graph of a cube root function looks like a stretched out ______

Correct Answer: S

Question 9:

The radicand of a radical expression is the expression ______ the radical symbol.

Correct Answer: under

Question 10:

The domain of f(x)=√(2x+6) is x≥ ______.

Correct Answer: -3

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.1.7:Graph a radical function (square root and cube root only). Identify the domain, range, and x- and y-intercepts using various methods and tools that may include a graphing calculator or other appropriate technology.

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