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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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In mathematics, an equation is an equation that expresses two equations by joining them with an equal sign =. Equations in other languages ​​and the word their relatives can have slightly different meanings; for example, in French, an equation is defined as containing one or more variables, but in English, it is an equal sign.

A well-formed expression consisting of two combined equations is an equation, and a variable makes the equation true. The variable for which the equation must be solved is also called the unknown, and the value of the unknown that satisfies the equation is called the solution of the equation. There are two types of equations: identities and constraint equations. The ID applies to all values ​​of the variable. Constraint equations apply only to specific values ​​of variables

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