When conducting a survey, it is important to use a random sample:to get a significant result.to avoid bias and to get a represen
1 answer:
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Answer:
see details in graph and below
Step-by-step explanation:
There are many ways to generate the function.
We'll generate a function whose first derivative f'(x) satisfies the required conditions, say, a quadratic.
1. f(x) has a local minimum at x = -3, and
2. a local maximum at x = 3
Therefore f'(x) has to cross the x-axis at x = -3 and x=+3.
Furthermore, f'(x) must be increasing at x=-3 and decreasing at x=+3.
f'(x) = -x^2+9
will satisfy the above conditions.
Finally f(x) must be decreasing at x= -5, which implies that f'(-5) must be negative.
Check: f'(-5) = -(-5)^2+9 = -25+9 = -16 < 0 so ok.
f(x) can then be obtained by integrating f'(x) :
f(x) = integral of -x^2+9 = -x^3/3 + 9x = 9x - x^3/3
A graph of f(x) is attached, and is found to satisfy all three conditions.
Answer:
- distance to x-axis: 3 units
- distance to y-axis: 2 units
- the reflected point is (2, 3)
Step-by-step explanation:
The given point is (-2, 3), labeled point A in the attachment.
As you know, the distance from the x-axis is given by the y-coordinate. Here, that distance is ...
3 units from the x-axis
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The distance from the y-axis is given by the magnitude of the x-coordinate. Here, that distance is ...
2 units from the y-axis
Note that the negative coordinate value means the point is located that distance to the left of the y-axis.
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Reflecting the point across the y-axis means choosing a point that is the same distance (2 units) right of the axis instead of left of the axis. The sign of the x-coordinate value will be positive, instead of negative. (The y-coordinate remains unchanged,)
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The reflected point is (2, 3).
_____
<em>Additional comment</em>
As we have seen, reflection across the y-axis changes the sign of the x-coordinate:
(x, y) ⇒ (-x, y) . . . . reflection across the y-axis
Similarly, reflection across the x-axis changes the sigh of the y-coordinate:
(x, y) ⇒ (x, -y) . . . . reflection across the x-axis
