Help me out please ...
2 answers:
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Answer:
This relation represent y as a function of x, because each value of x is associated with a single value of y
Step-by-step explanation:
we know that
A function is a relation from a set of inputs (x values) to a set of possible outputs (y values) where each input is related to exactly one output
we have the relation
This relation represent y as a function of x, because each value of x is associated with a single value of y
The function is divided in 2 parts:
For x<0, the function is
, which is a linear function, and its graph is a line.
For x≥0, the function is
, which is a quadratic function, and its graph is a parabola.
Note that y=x is the line containing the points (0, 0), (1, 1), (5, 5) etc, that is, it is the line passing through the origin, with an inclination of 45° with the positive x-axis.
The parabola is the parabola 
reflected with respect to the x-axis. It contains points like (0, 0), (-1, 1), (2, -4) etc...
The 2 graphs, with domain all real numbers, are shown in the first picture.
The second picture is the graph of the function described in our problem. We use the first picture, but restrict the domains.
That is, we delete the part of the line corresponding to x≥0, and the part of the parabola corresponding to x<0.
For x<0, the function is
For x≥0, the function is
Note that y=x is the line containing the points (0, 0), (1, 1), (5, 5) etc, that is, it is the line passing through the origin, with an inclination of 45° with the positive x-axis.
The parabola
The 2 graphs, with domain all real numbers, are shown in the first picture.
The second picture is the graph of the function described in our problem. We use the first picture, but restrict the domains.
That is, we delete the part of the line corresponding to x≥0, and the part of the parabola corresponding to x<0.