consider the graph of f(x). © 2020 strongmind. created using geogebra. which statements are true about the…

consider the graph of f(x). © 2020 strongmind. created using geogebra. which statements are true about the function represented by the graph? select all that apply. the function decreases over the intervals (-∞, -2) and (2, 3). the function increases over the intervals (-2, 2) and (3, ∞). the function increases over the interval (-0.5, 2.5). the function decreases over the intervals (-∞, -0.5) and (2.5, ∞). the function increases over the intervals (-∞, -0.5) and (2.5, ∞). the function decreases over the interval (-0.5, 2.5).

consider the graph of f(x). © 2020 strongmind. created using geogebra. which statements are true about the function represented by the graph? select all that apply. the function decreases over the intervals (-∞, -2) and (2, 3). the function increases over the intervals (-2, 2) and (3, ∞). the function increases over the interval (-0.5, 2.5). the function decreases over the intervals (-∞, -0.5) and (2.5, ∞). the function increases over the intervals (-∞, -0.5) and (2.5, ∞). the function decreases over the interval (-0.5, 2.5).

Answer

Explanation:

Step1: Analyze increasing - decreasing intervals

For a function (y = f(x)), if the graph goes up as (x) increases, the function is increasing; if the graph goes down as (x) increases, the function is decreasing.

Step2: Check each interval

  • Looking at the graph, as (x) moves from (-\infty) to (- 2), the graph is going down, so the function is decreasing on ((-\infty,-2)).
  • As (x) moves from (-2) to (2), the graph is going up, so the function is increasing on ((-2,2)).
  • As (x) moves from (2) to (3), the graph is going down, so the function is decreasing on ((2,3)).
  • As (x) moves from (3) to (\infty), the graph is going up, so the function is increasing on ((3,\infty)).
  • On the interval ((-0.5,2.5)), the graph first goes down from (x=-0.5) to (x = 2.5), so the function is decreasing on ((-0.5,2.5)).

Answer:

The function decreases over the intervals ((-\infty,-2)) and ((2,3)); The function increases over the intervals ((-2,2)) and ((3,\infty)); The function decreases over the interval ((-0.5,2.5))