Calculate the positive domain of the function shown in the figure:
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Calculate the positive domain of the function shown in the figure:
The domains of positivity and negativity are determined by the point of intersection of the function with the X-axis, so the Y values are greater or less than 0.
We are given the information of the intersection with the Y-axis, but not of the point of intersection with the X-axis,
Furthermore, there is no data about the function itself or the slope, so we do not have the ability to determine the point of intersection with the X-axis,
And so in the domains of positivity and negativity.
Not enough data
What is the solution to the following inequality?
\( 10x-4ā¤-3x-8 \)
The point (0, 4) only tells you where the line crosses the y-axis. To find where the function is positive (above the x-axis), you need to know where it crosses the x-axis - that's the boundary between positive and negative regions!
You would need either:
Ask yourself: "Can I write the complete equation of the line?" For a linear function, you need two pieces of information (like two points, or one point and the slope). If you can't write completely, you likely need more data.
Absolutely! In real mathematics, recognizing when you don't have sufficient information is just as important as solving problems. It shows you understand what's required to find a solution.
If the line crossed the x-axis at point (a, 0), then:
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