Given the function of the graph.
What are the areas of positivity and negativity of the function?
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Given the function of the graph.
What are the areas of positivity and negativity of the function?
When we are asked what the domains of positivity of the function are, we are actually being asked at what values of X the function is positive: it is above the X-axis.
At what values of X does the function obtain positive Y values?
In the given graph, we observe that the function is above the X-axis before the point X=7, and below the line after this point. That is, the function is positive when X>7 and negative when X<7,
And this is the solution!
Positive
Negative
Look at the linear function represented in the diagram.
When is the function positive?
Areas of positivity are the x-values where the function gives positive y-values. Look at where the graph sits above the x-axis - those are your positive regions!
Follow the line from left to right! When the line is above the x-axis, the function is positive. When it's below the x-axis, it's negative. The crossing point at x=7 is where it changes sign.
Look at the graph carefully! The line starts high on the left (positive y-values) and slopes downward, crossing the x-axis at x=7. So for x-values less than 7, the function is above the axis (positive).
At x=7, the function equals zero because that's where the line crosses the x-axis. This point is neither positive nor negative - it's the boundary between the positive and negative regions.
Pick test points! Choose an x-value less than 7 (like x=5) and see if the graph shows a positive y-value there. Then pick an x-value greater than 7 (like x=9) and check if it's negative. This confirms your regions! ✓
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