Module 2: Lesson 2

 

Self-Check 1

 

Question 4 on page 87

  1.  
    1. This shows the graphs of two functions. The first function is f at x equals 4 minus x. The second function is f at x equals begin the square root of 4 minus x end of the square root. The graphs intersect at the points (4, 0) and (3, 1).
    2. The graph can be split up into four regions:
      • When 4 − x < 0, then is undefined.
      • When 0 < 4 − x < 1, then
      • When 4 − x > 1, then
      •  when y = 0 and y = 1. (These are the invariant points.)

    3. For f(x) = 4 − x:

       
      Domain: {x|x ∈ R}

      Range:

      		 {y|y ∈ R}

      In the graphs of square root functions, the domains of the square root function are restricted in the areas of the original graph where y < 0: any portion of the original graph that lies below the x-axis will not appear in the graph of the square root of the function. In this case, that occurs when x > 4 and when y < 0. As a result, for

       
      Domain: {x|x ≤ 4, x ∈ R}

      Range:

      		 {y|y ≥ 0, y ∈ R}

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