Question

Use the graph to answer the question.A student was given the piecewise function (in pic) and created this graph of the function.Is the student's graph a correct representation of the function? If not, explain how it should be corrected.

Answer 1

Firstly, the student's graph is not a correct representation of the piecewise function, We would consider each function.

1. f(x) = x + 3 for x ≤ - 2

The graph is correct but the interval was not represented correctly. To correct it, the circle at x = 2 should be solid

2) f(x) = x^2 - 1 for - 2 < x < 1

The graph is correct but the interval was not represented correctly. To correct it, the circles at x = - 2 and x = 1 shouldn't be solid

3) f(x) = log2(- x + 3) for 1 ≤ x < 3

The graph is not correct. To correct it, values of x should be substituted into the function and the correct values of y or f(x) would be calculated for. These values of x and y should be used to plot the graph again. For the intervals, the circle at x = 1 should be solid while the circle at x = 3 shouldn't be solid