Question

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

Answer 1

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 graph of the function

The piecewise function is given as:

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

See attachment for the graph of the piecewise function.

The x-intercepts 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

The intervals where g(x) is positive

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)

Read more about piecewise function at:

brainly.com/question/11827078

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