A piecewise function g(x) is defined by g(x)={x^3-4x for x<2, -log_4(x-1)+2 for x>=2

Part A: graph the piecewise function g(x) and determine the domain

Part B: determine the x-intercepts of g(x). Show all necessary calculations.

Part C: Describe the interval(s) in which the graph of g(x) is positive.

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MrRoyal MrRoyal · Answer 1 · 2022-06-14T08:30:28+02:00

The x-intercepts of the piecewise function are 1.59 and 17 and the intervals where g(x) is positive are (-2,0) and [2,17)

The piecewise function is given as:

[tex]g(x) = \left[\begin{array}{cc}x^3-4x &x < 2\\-\log_4(x - 1) + 2 &x \ge 2\end{array}\right[/tex]

See attachment for the graph of the piecewise function.

This is the point where the piecewise function crosses the x-axis.

From the attached graph, the graph crosses the x-axis at x = -2, x = 0 and x = 17

Hence, the x-intercepts of the piecewise function are -2, 0 and 17

This is the range of x value where g(x) > 0

From the attached graph, g(x)> 0 between x = -2 & x = 0 and between x = 2 (inclusive) & x = 17

Hence, the intervals where g(x) is positive are (-2,0) and [2,17)

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