Question

Explain how to graph the given piecewise-defined function. Be sure to specify the type of endpoint each piece of the function will have and why. f(x) = StartLayout enlarged left-brace 1st Row 1st column negative x + 3, 2nd column x less-than 2 2nd row 1st column 3, 2nd column 2 less-than-or-equal-to x less-than 4 3rd Row 1st column 4 minus 2 x, 2nd column x greater-than-or-equal-to 4 EndLayout

Answer 1

For input values below 2, the f(x) = -x + 3 function would be shown on a graph. Given that the first piece's domain does not consist of (2, 1), the point (2, 1) would be open. You would then graph a horizontal line at f(x) = 3 for input values between 2 and 4. At (2, 3) a circle would be closed, but at (4, 3), a circle would be open. In the end, you'd plot f(x) = 4 - 2x for x values above 4. Since 4 is in the domain of the third piece, a closed circle would be at (4, -4).

Explanation:

Rephrased Sample Response | Correct on EDGE 2023

Answer 2

sample response You would graph the equation f(x) = –x + 3 for input values less than 2. There would be an open circle at the point (2, 1) since the domain for the first piece does not include 2. You would then graph a horizontal line at f(x) = 3 for input values between 2 and 4. There would be a closed circle at (2, 3) and an open circle at (4, 3). Last, you would graph f(x) = 4 – 2x for input values greater than or equal to 4. There would be a closed circle at the point (4, –4) since 4 is in the domain of the third piece.

Explanation: