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<h2>Hello!</h2>
The answer is:
The second piecewise function,
To answer the question, we need to find which piecewise function contains the graphs shown in the picture, we have that first line shown, is decreasing and exists from the negative numbers to 0, and the line cuts the x-axis and the y-axis at "-2", for the second line shown, we have that is decreasing but exists from 0 (including it) to the the positive numbers.
So, finding which piecewise satisfies the function shown, we have:
- First piecewise function:
First line,
We have the first line,
The variable has a negative coefficient (-1), meaning that the function (line) is decreasing, also we can see that the function does exists from all the numbers less than 0, to 0, and it cuts the x-axis at -2 and the y-axis at -2.
Second line,
The variable has positive coefficient, meaning that the function (line) is increasing.
Hence, since the second line is not decreasing, the piecewise function is not the piecewise function shown in the picture.
- Second piecewise function,
First line,
We have the first line,
The variable has a negative coefficient (-1), meaning that the function (line) is decreasing, also we can see that the function does exist from all the numbers less than 0, to 0.
Second line,
The variable has a negative coefficient (, meaning the the unction (line) is decreasing, also we can see that the function does exists from 0 (including it) to the positive numbers.
Hence, we have that the correct option is the second piecewise function,
Note: I have attached a picture for better understanding.
Have a nice day!