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MA_775_DIABLO [31]
1 year ago
8

Question in the photo

Mathematics
1 answer:
yaroslaw [1]1 year ago
8 0

Using translation concepts, the equation of g(x) is given as follows:

g(x) = -\frac{35}{x + 10} - 1

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the parent function is given by:

f(x) = \frac{1}{x}

For a horizontal compression by a factor of 1/5, we have to find f(1/5x), hence:

g(x) = \frac{1}{\frac{1}{5}}x = \frac{5}{x}

For a vertical stretch by a factor of 7, we have to multiply by 7, hence:

g(x) = \frac{35}{x}

For a reflection in the y-axis, we have to find g(-x), hence:

g(x) = \frac{35}{-x} = -\frac{35}{x}

For a translation of 10 units left, we have to find g(x + 10), hence:

g(x) = -\frac{35}{x + 10}

For a translation of 1 unit down, we have to subtract one, hence:

g(x) = -\frac{35}{x + 10} - 1

More can be learned about translation concepts at brainly.com/question/28174785

#SPJ1

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1.2, 3, 7.5, 18.75, ...<br><br> Which formula can be used to describe the sequence?
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Answer:

The formula is:

a_n=1.2(\frac{5}{2})^{n-1}

Step-by-step explanation:

The geometric sequences are those in which the division between the terms a_{n + 1} and a_n of the sequence are equal to a constant common reason called "r"

The geometrics secencias have the following form:

a_n=a_1(r)^{n-1}

Where a_1 is the first term of the sequence

In this sequence we have the following terms

1.2, 3, 7.5, 18.75

Then notice that:

\frac{3}{1.2}=\frac{5}{2}\\\\\frac{7.5}{3}=\frac{5}{2}\\\\\frac{18.75}{7.5}=\frac{5}{2}

Then:

r=\frac{5}{2}  and a_1=1.2

Finally the formula is:

a_n=1.2(\frac{5}{2})^{n-1}

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