given the function ( h(x) ), over which of the following intervals is ( h ) only increasing? ( -3 lt x lt 3…

given the function ( h(x) ), over which of the following intervals is ( h ) only increasing? ( -3 lt x lt 3 ) ( 1 lt x lt 4 ) ( -1 lt x lt 4 ) ( -3 lt x lt 1 )

given the function ( h(x) ), over which of the following intervals is ( h ) only increasing? ( -3 lt x lt 3 ) ( 1 lt x lt 4 ) ( -1 lt x lt 4 ) ( -3 lt x lt 1 )

Answer

Answer:

$-3 < x < 1$

Explanation:

Step1: Understand the concept of increasing function

A function (y = h(x)) is increasing if as (x) increases, (y) also increases. On a graph, this means the function has a positive - slope.

Step2: Analyze each interval

  • For the interval (-3 < x < 3): The function first decreases (negative slope) and then increases (positive slope) and then decreases (negative slope) again. So, it is not only increasing in this interval.
  • For the interval (1 < x < 4): The function is decreasing (negative slope) in this interval.
  • For the interval (-1 < x < 4): The function first increases (from (x=-1) to (x = 1)) and then decreases (from (x = 1) to (x=4)). So, it is not only increasing in this interval.
  • For the interval (-3 < x < 1): Looking at the graph, as (x) moves from (-3) to (1), the (y) - values of the function (h(x)) are continuously increasing. The slope of the function in this interval is positive.