MHB Overcoming Struggles to Addressing Inequalities Step by Step

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The discussion focuses on the challenges of understanding inequalities in mathematical functions. Participants express a desire for a step-by-step approach to grasp these concepts better. The conversation highlights the significance of the function f(x) in determining the values above, on, or below the x-axis. Clarifications are sought regarding the specific inequalities related to a particular item, emphasizing the relationship between f(x) and y values. Overall, the thread aims to provide guidance on overcoming struggles with mathematical inequalities.
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I’m overall struggling. Not liking the inequalities. Any step by step would be awesome
 

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$f(x) > 0$ is any part of the graph that is above the x-axis

$f(x) = 0$ is any part of the graph that crosses or touches the x-axis

$f(x) < 0$ is any part of the graph below the x-axis
 
Beer soaked query follows.
Seka88 said:
I’m overall struggling. Not liking the inequalities. Any step by step would be awesome
D97F9FC9-ABA4-4A78-956C-B889286E4D18.jpeg

Is there a specific inequality behind item #5?
 
Do you not understand that in "y= f(x)" any value of f is a "y" value? f(x)= 0 means y= 0 so that is a point on the x- axis. That is what goes into the first two blanks. For the other two we need to know how "f(x)" is defined here.
 
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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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