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lions [1.4K]
2 years ago
6

How to answer this piecewise function?

Mathematics
2 answers:
inysia [295]2 years ago
8 0
<h3>Answer: -2*g(x) + 2</h3>

This shifts the graph down 1 unit, reflects over the x axis, then vertically dilates by a factor of 2.

=============================================================

Explanation:

Refer to the figures below. The screenshots may be a bit on the big side, so brainly might attempt to reduce the size. To fix this, click on the magnifying glass to get a better look. There are 4 images in total.

Figure 1 is the original graph your teacher gave you.

Figure 2 shows the translation of the parabola 1 unit down. This aligns the right piece of the red parabola to the green V curve. This junction location is (1,0).

Afterward, in figure 3, we reflect the parabola over the x axis to have the left endpoint of the parabola (-3,8) move to (-3,-8). Unfortunately the (-3,-8) doesn't match up with the right most piece of the blue cubic curve.

Luckily, a quick fix is to double the y coordinate from -8 to -16 and the two pieces match perfectly. The other junction is (-3,-16). This is shown in figure 4.

To summarize, we did these transformations in the order presented.

  1. Shift down 1 unit (figure 2)
  2. Reflect over the x axis (figure 3)
  3. Vertically stretch or dilate by a factor of 2 (figure 4)

--------------

Now to shift down 1 unit, we subtract 1 from each g(x) output.

Therefore, we go from g(x) to g(x)-1

Reflect over the x axis to get -(g(x) - 1) = -g(x) + 1

Lastly, we double everything when applying the dilation mentioned to end up with the final answer:  -2*g(x) + 2

You can use a tool like GeoGebra to check your work. It's the app I used to make the figures shown below.

Ber [7]2 years ago
4 0

Answer:

well the answer is... and then you... which leads to.....

Step-by-step explanation:

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Given the points A(-10, -4) and B(14, 4), find the coordinates of the point P on the directed line segment AB that partitions AB
anastassius [24]

Answer:

P(5, 1)

Step-by-step explanation:

Segment AB is to be partitioned in a ratio of 5:3. That means the ratio of the lengths of AP to PB is 5:3. We need to find the ratio of the lengths of AP to AB.

AP/PB = 5/3

By algebra:

PB/AP = 3/5

By a rule of proportions:

(PB + AP)/AP = (3 + 5)/5

PB + AP = AP + PB = AB

AB/AP = 8/5

AP/AB = 5/8

The first part of the segment is 5/8 of the length of the segment, and the second part of the segment has length of 3/8 of the length of segment AB.

Point P is located 5/8 of the distance from point A to point B. The x-coordinate of point P is 5/8 of the difference in x-coordinates added to the x-coordinate of point A. The y-coordinate of point P is 5/8 of the difference in y-coordinates added to the y-coordinate of point A.

x-coordinate:

difference in coordinates: |14 - (-10)| = |14 + 10| = 24

5/8 of 24 = 5/8 * 24 = 15

Add 15 to the x-coordinate of point A: -10 + 15 = 5

x-coordinate of point P: 5

y-coordinate:

difference in coordinates: |4 - (-4)| = |4 + 4| = 8

5/8 of 8 = 5/8 * 8 = 5

Add 5 to the y-coordinate of point A: -4 + 5 = 1

y-coordinate of point P: 1

Answer: P(5, 1)

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3 years ago
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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

(8×8) + (15×15) = 289

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