Please help asap. it’s 2 am and idk how to do this

Mathematics

1 answer:

lesya692 [45]3 years ago

5 0

This is an example of a piecewise defined function. It means that the function has not a unique formula to represent it, but it depends on "where" you want to compute it.

So, if you choose any input $x$ , you have two alternative:

If $x \neq 3$ (i.e., if you've chosen any input that is not 3), the output will be the opposite of the input you've chosen ( $y=-x$ )
If $x=3$ , the ouput will be -1.

So, let's forget about $x=3$ for a moment. For any input $x$ you choose, the answer is $-x$ . The graph of this function is the bisector of the second and fourth quadrant.

Now remember that there is our special case: you have to "carve a hole" in our line, at $x=3$ , and assing to this point the value -1, instead of what we would expect, i.e. -3.

So, the graph of this function is the line $y=-x$ , except for one point ( $x=3$ ), where we reassign the value to be -1.

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Find the distance between the points.<br> (r, s) and (0, 0)

zhenek [66]

Answer: $\sqrt{r^2+s^2$

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Reason:

Plot the points (0,0) and (r,s). You can place (r,s) anywhere you want.

Connect the two points mentioned and form a right triangle such that the segment from (0,0) to (r,s) is the hypotenuse of said right triangle.

The horizontal leg has a length of r-0 = r units, while the vertical leg will be 's' units.

Check out the diagram below.

We then apply the pythagorean theorem to say $r^2+s^2 = h^2$ where h is the hypotenuse. Solving for h gets us $h = \sqrt{r^2+s^2}$ . We only focus on the positive square root since a negative hypotenuse makes no sense.

Since we made the hypotenuse the segment with endpoints (r,s) and (0,0), this means the hypotenuse length and the distance are the same thing.

Therefore, the distance from (r,s) to (0,0) is $\sqrt{r^2+s^2}$

As an alternative, you can use the distance formula to get the same answer. The distance formula is effectively the pythagorean theorem phrased a different way.