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chubhunter [2.5K]
3 years ago
13

Identify the domain of the exponential function shown in the following graph. Explain how you know.

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
6 0

Answer:

The domain of the function is R i.e. any real value.

Step-by-step explanation:

The given figure is a graph on the coordinate plane of the function y = 10^{x}

Now, the domain of a function means that the values of x (Independent variable) for which the function is valid i.e. the y values are real.

It is clear from the equation given above that for any real value of x there will be a real corresponding value of y.

Therefore, the domain of the function is R i.e. any real value. (Answer)

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What value of y would make {(-2, 18), (3, y), (6, 6), (-18, 2), (4, 9)} an inverse variation?​
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Answer:

The value of "y" the would make the ordered pairs an inverse variation is;

y = 12

Step-by-step explanation:

The given ordered pairs are;

{(-2, 18), (3, y), (6, 6), (-18, 2), (4, 9)}

When a pair of variables, "x" and "y", vary inversely to one another, as the value of one variable increases, the value of the other variable decreases

Mathematically, we have;

y ∝ 1/x

The above relation can be represented as an equation as follows;

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Where;

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From the given ordered, we have;

k =  -2 × 18 = -36

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Therefore, the value of "k" is made constant as follows;

The inverse variation is y = k/(x × (-1)ⁿ)

Where;

n = The number of the term

Therefore, y = 36/(3 × (-1)²) = 12

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The given ordered pairs can therefore be written as follows;

{(-2, 18), (3, 12), (6, 6), (-18, 2), (4, 9)}.

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