The slope of the function on the graph is 1.
What is the negative domain of the function?
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The slope of the function on the graph is 1.
What is the negative domain of the function?
To answer the question, let's first remember what the "domain of negativity" is,
The domain of negativity: when the values of Y are less than 0.
Note that the point given to us is not the intersection point with the X-axis but with the Y-axis,
That is, at this point the function is already positive.
The point we are looking for is the second one, where the intersection with the X-axis occurs.
The function we are looking at is an increasing function, as can be seen in the diagram and the slope (a positive slope means that the function is increasing),
This means that if we want to find the point, we have to find an X that is less than 0
Now let's look at the solutions:
Option B and Option D are immediately ruled out, since in them X is greater than 0.
We are left with option A and C.
Option C describes a situation in which, as X is less than 0, the function is negative,
Remember that we know the slope is 1,
Which means that for every increase in X, Y also increases in the same proportion.
That is, if we know that when (0,1) the function is already positive, and we want to lower Y to 0,
X also decreased in the same value. If both decrease by 1, the resulting point is (0,-1)
From this we learn that option C is incorrect and option A is correct.
Whenever X is less than -1, the function is negative.
Look at the linear function represented in the diagram.
When is the function positive?
The negative domain is the set of x-values where the function's y-values are negative (below the x-axis). It's asking: 'For which x-values is y < 0?'
Because the function doesn't become negative until x < -1! At x = 0, y = 1 (positive). The function crosses the x-axis at x = -1, so it's only negative when x < -1.
Use the slope and y-intercept! Start at (0,1), then use slope = 1 to go backwards: decrease x by 1 and decrease y by 1. This gives you (-1,0) as the x-intercept.
The method stays the same! Use the slope to find the x-intercept from the y-intercept. For example, with slope 2 and y-intercept (0,1), you'd get x-intercept at .
Test a point! Pick any x-value less than -1 (like x = -2) and calculate y. If y is negative, your domain is correct. For x = -2: y = -2 + 1 = -1 (negative) ✓
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