Question

A piecewise function g(x) is defined by g of x is equal to the piecewise function of x cubed minus 16 times x for x is less than 4 and negative log base 4 of the quantity x minus 3 end quantity plus 2 for x is greater than or equal to 4 Part A: Graph the piecewise function g(x) and determine the domain. (5 points) Part B: Determine the x-intercepts of g(x). Show all necessary calculations. (5 points) Part C: Describe the interval(s) in which the graph of g(x) is positive. (5 points)

Answer 1

Using function concepts and the graph, it is found that:

a) The graph is given at the end of this answer.

b) The x-intercepts are x = -4, x = 0 and x = 19.

c) The function is positive in the intervals $(-4,0) \cup (4,19)$.

-----------------------------

Item a:

The piece-wise function is defined by:

$g(x) = x^3 - 16x, x < 4$

$g(x) = -\log_{4}{x - 3} + 2, x \geq 4$

At the end of this answer, the graph is given.

-----------------------------

Item b:

The x-intercepts are the values of x for which y = 0.

From the graph, they are: x = -4, x = 0 and x = 19.

-----------------------------

Item c:

• The function is positive when it is above the horizontal axis, thus in the intervals $(-4,0) \cup (4,19)$

A similar problem is given at brainly.com/question/24313105