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Describe analytically (in terms of equation)
The set of points parallel to the x-axis and 5 units away from the point (2,2) (TWO ANSWERS)

Sagot :

The horizontal graph parallel to the x-axis is described by equation:
    y = b,  where b is the y-intercept at (0,y), and slope (m) = 0.

1)  The equation 5 units above the point (2,2):
      To find the y-intercept given the points, when y=2:
      y- intercept  (b) = 2 + 5
      y - intercept  (b) = 7  

      Since the equation for horizontal graph is y = b, therefore the equation 5 units above point (2,2) is:

      y = 7
    
2.)  5 units below the point (2,2):
      To find the y-intercept given the points, when y=2:
      y-intercept (b) =  2 - 5
      y - intercept (b) = -3
     
      Since the equation for the horizontal graph is y = b, therefore, the equation 5 units below point (2,2) is:
    
       y = -3

ANSWER:
1)  y = 7
     m (slope) = 0
     Domain = {x / x is an element of real numbers}
     Interval notation:  (⁻∞ , ⁺∞)
     Range = {y / y = 7}
                 =  {7}

2) y = -3
    m (slope) = 0
    Domain = {x / x is an element of real numbers}
    Interval notation: (⁻∞,  ⁺∞)
    Range = {y / y= -3}
                = {3}

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