Use the graph of function g to answer these questions.
(A) What are the values of , g(1) ,g(-12) and g(15)?
(B) For what x-values is g(x) = -6 ?
(C) Complete the rule for g(x) so that the graph represents it.
(A) Trace a vertical line from x = 1, it intersects with the graph at y = 4. Therefore, g(1) = 4. For x = -12, the vertical line intersects with the graph at y = -10, therefore, g(-12) = -10. For x = 15, the vertical line does NOT intersect with the graph since g(x) is not determined for x= 15. g(15) is NOT defined.
(B) The graph has a value of y = -6 for all values of -8 <= x < -1. Important to note the <= (less than or equal to) since the circle is filled in. Note that if you trace a vertical line for any value of x between -8 and -1 the line will intersect with the graph at y = -6.
(C) To complete this, look at what the value of g(x) is for -10 <= x < -8. It is y = -8. Find what the value of g(x) is for -1 <= x < 1. It is y = 2. And finally, determine for what values of x is g(x) = 4, we see that for 1 <= x < 10, g(x) = 4. Therefore, the rule is
g(x) = -10 for -15 <= x < -10
g(x) = -8 for -10 <= x < -8
g(x) = -6 for -8 <= x < -1
g(x) = 2 for -1 <= x < 1
g(x) = 4 for 1 <= x < 10
g(x) = 8 for 10 <= x < 15
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