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Answer :
The equation that represents the function graphed on the coordinate plane is g(x) = |x - 21 - 4| , which corresponds to option c.
To determine which equation represents the function graphed on the coordinate plane, let's analyze the key features of the graph.
The equation of the graph involves the absolute value function, and it appears to be shifted horizontally and vertically.
The general form of the absolute value function is f(x) = |x-h| + k , where ( h ) is the horizontal shift (left or right) and k is the vertical shift (up or down).
Looking at the graph, it appears that the graph is shifted 21 units to the right and 4 units upwards. So,( h = 21 ) and ( k = 4 ).
Now, comparing the options:
a. g(x) = x + 41 - 2 - This equation represents a linear function, not an absolute value function.
b. g(x) = |x - 41 - 2| - This equation represents the absolute value function with a horizontal shift of 41 units to the right and a vertical shift of 2 units downwards. It doesn't match the graph.
c. g(x) = |x - 21 - 4| - This equation represents the absolute value function with a horizontal shift of 21 units to the right and a vertical shift of 4 units upwards. This seems to match the graph.
d. g(x) = |x - 21 + 4| - This equation represents the absolute value function with a horizontal shift of 21 units to the right and a vertical shift of 4 units downwards. It doesn't match the graph.
So, the equation that represents the function graphed on the coordinate plane is g(x) = |x - 21 - 4| , which corresponds to option c.
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