1. Lesson 3

1.7. Explore 3

Mathematics 30-1 Module 2

Module 2: Radical Functions

 

In Try This 3 you may have produced a graph like this.

 

This shows a graph of the functions y equals begin square root 2 times x squared subtract 3 end square root and y equals x with the intersection point (1.73, 1.73) labelled.

 

The solution is the x-value at the intersection point of the two graphed functions. Graphically, there is only one solution, approximately 1.73. Algebraically, there were two solutions, , with one solution being an extraneous root, .

 

In Try This 3 you may have reached the following conclusions:

  • The graphical solution is the same as the algebraic solution.
  • The algebraic solutions can be given as exact values or approximate values.
  • The graphical solutions are given as approximate values.
  • The algebraic solutions may have extraneous solutions. The graphical solutions are never extraneous solutions.
Self-Check 2

 

textbook

  1. Review “Example 3” on pages 93 and 94 of the textbook. Answer the following questions based on the example.
    1. For Method 1, what is the step you must take before you create the graph? How do you find the solution? Answer
    2. For Method 2, what is the step you must take before you create the graph? How do you find the solution? Answer
    3. Which graphical method do you prefer? Why? Answer
  2. Complete “Your Turn” after “Example 3” on page 94 of the textbook. Answer
  3. Complete question 2 on page 102 of the textbook. Answer