Find the formula for the function.

A point P in the fourth quadrant lies on the graph of the function f(x) = -x2. Express the slope of the line joining P to the origin as a function of x.

Question

Find the formula for the function.

A point P in the fourth quadrant lies on the graph of the function f(x) = -x2. Express the slope of the line joining P to the origin as a function of x.

BlackTom AI · Accepted Answer

The problem asks for the slope of the line joining the origin to a point P on the graph of f(x) = -x^2 in the fourth quadrant.

First, identify the coordinates of P. Since P lies on the graph, its coordinates are (x, f(x)) = (x, -x^2).

Next, compute the slope m of the line from the origin (0,0) to P(x, -x^2) using the slope formula m = (y2 - y1) / (x2 - x1).
- Here, (x1, y1) = (0,0) and (x2, y2) = (x, -x^2).
- Therefore, m = (-x^2 - 0) / (x - 0) = (-x^2) / x = -x, provided x ≠ 0.

Now evaluate the given answer choices:

Option 1: "m =" — This is incomplete and does not express the slope, so it cannot be correct.

Option 2: "m = -x" — This matches the derived expression for the slope, so this is correct.

Option 3: "m = -2x" — This would arise from an incorrect manipulation or misapplication of a derivative-like step, not from the slope formula here, so it is incorrect.

Option 4: "m = x" — This has the wrong sign and direction compared to the actual slope from the origin to (x, -x^2) in the fourth quadrant, so it is incorrect.

In summary, the slope from the origin to P computes to -x, which aligns with the coordinate setup where x > 0 and y < 0 in the fourth quadrant. The other options fail due to incompleteness, miscalculation, or sign error.

MATH2415W16 Practice Quiz- Requires Respondus LockDown Browser

Find the formula for the function. A point P in the fourth quadrant lies on the graph of the function f(x) = -x2. Express the slope of the line joining P to the origin as a function of x.

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MATH*2415*W16 Practice Quiz- Requires Respondus LockDown Browser

Find the formula for the function. A point P in the fourth quadrant lies on the graph of the function f(x) = -x2. Express the slope of the line joining P to the origin as a function of x.

View Explanation

Log in for full answers

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MATH2415W16 Practice Quiz- Requires Respondus LockDown Browser