Answer :
The function g(x) is greater than zero when the value of x lies in between -3 and 5 and this can be determined by using the given graph.
Given :
The graph of the function g(x) is given.
The following steps can be used in order to determine the interval for g(x):
Step 1 - The value of g(x) means the value of y.
Step 2 - The value of g(x) is positive when the graph of g(x) is in the first or in the second quadrant.
Step 3 - So, according to the graph function g(x) is positive when the value of x is in between -3 and 5.
Therefore, the correct option is 3).
For more information, refer to the link given below:
https://brainly.com/question/5245372
Final answer:
To determine where g(x) > 0 without a provided graph, one would examine the signs of the numerator and denominator for a rational function, or use test points for other functions, looking for intervals where the function is above the x-axis.
Explanation:
The question refers to determining the intervals where the function g(x) is greater than zero (g(x) > 0). To find these intervals, one would typically look at a graph of the function and identify the regions where the function's curve is above the x-axis. Without an actual graph to refer to, we can imagine plotting the function and looking for these positive intervals. For a function represented by an equation, we can determine these intervals by analyzing the signs of the numerator and denominator for rational functions or by using test points in intervals for other types of functions.
If we were to consider the example function f(x) = x(3 - 4x)/(1 + x²), we would find intervals of positivity by determining where both the numerator and denominator are positive or both are negative, which results in a positive value for f(x). However, it is important to note that the intervals we're looking for the original question about g(x) must be identified from the actual graph provided with the question.
