Question

How do you do this?

Answer 1

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Answer:

  see attached for 1 and 2

Step-by-step explanation:

It's almost like drawing any other graph. Here, you need to pay attention to the domain on which each piece is defined. You need to add dots where the function is discontinuous to show how the function is defined at the discontinuity.

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1) The dividing line is at x=2.

To the left of that line, the graph is the constant function y=3.

To the right of that line, the graph is the quadratic function y = (x-3)².

The dots are placed where x=2 (at the boundary between the parts of the function). A solid dot is placed on the end of the horizontal line, since that is the function value at x=2. An open dot is placed on the end of the parabola, since the function is not defined at that point (2, 1).

The graph is shown in the first attachment.

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2) Here, the dividing line between the pieces is at x=-4. Again, the function is constant to the left of that line. To the right of that line, it is a line with a slope of 2 and a y-intercept of 3. The treatment of dots at the ends of the curve is the same, since the function is defined at x=-4 as the left piece, not the right piece.

The graph is shown in the second attachment.