graphs and key features\nidentify the following for the given graph in any notation\ndomain:\nrange:\nincreas…

graphs and key features\nidentify the following for the given graph in any notation\ndomain:\nrange:\nincreasing:\ndecreasing:\npositive:\nnegative:\nx intercepts:\ny intercepts:

graphs and key features\nidentify the following for the given graph in any notation\ndomain:\nrange:\nincreasing:\ndecreasing:\npositive:\nnegative:\nx intercepts:\ny intercepts:

Answer

Explanation:

Step1: Determine Domain

The graph starts at ( x = -8 ) (from the leftmost point) and extends to the right, so domain is all real numbers from ( -8 ) to ( \infty ), i.e., ( [-8, \infty) ).

Step2: Determine Range

The lowest ( y )-value is ( -4 ) (at the vertex around ( x = 2 )) and it goes up, so range is ( [-4, \infty) ).

Step3: Determine Increasing Intervals

Find where the graph rises. From ( x = -8 ) to ( x = -2 ) (left peak) and from ( x = 2 ) to ( \infty ), so intervals ( (-8, -2) ) and ( (2, \infty) ).

Step4: Determine Decreasing Intervals

Find where the graph falls. From ( x = -2 ) to ( x = 2 ), so interval ( (-2, 2) ).

Step5: Determine Positive Intervals

Where ( y > 0 ). Between ( x = -4 ) (left root) and ( x = 0 ), and ( x > 6 ) (right root). So ( (-4, 0) \cup (6, \infty) ).

Step6: Determine Negative Intervals

Where ( y < 0 ). From ( x = -8 ) to ( x = -4 ), and ( x = 0 ) to ( x = 6 ). So ( [-8, -4) \cup (0, 6) ).

Step7: Determine X - intercepts

Points where ( y = 0 ). From graph, ( x = -4 ), ( x = 0 ), ( x = 6 ), so ( (-4, 0) ), ( (0, 0) ), ( (6, 0) ).

Step8: Determine Y - intercept

Point where ( x = 0 ), which is ( (0, 0) ).

Answer:

  • Domain: ( [-8, \infty) )
  • Range: ( [-4, \infty) )
  • Increasing: ( (-8, -2) \cup (2, \infty) )
  • Decreasing: ( (-2, 2) )
  • Positive: ( (-4, 0) \cup (6, \infty) )
  • Negative: ( [-8, -4) \cup (0, 6) )
  • X intercepts: ( (-4, 0) ), ( (0, 0) ), ( (6, 0) )
  • Y intercepts: ( (0, 0) )