3 years ago

Select the function that is even.

Mathematics

1 answer:

Katyanochek1 [597]3 years ago

8 0

Answer:

If I'm correct it should be f(x) = cos(x)

Step-by-step explanation:

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If the table represents an inverse variation, it means that y is inversely proportional to x, written as

$\begin{gathered} y\propto\frac{1}{x} \\ \propto is\text{ a sign of proportionality } \end{gathered}$

Removing the proportionality sign and introducing a constant k, we have

$\begin{gathered} y=k\times\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}$

In the first column, we have x = -4 and y = 3.5. Substituting these values for x and y, we have

$\begin{gathered} y=\frac{k}{x} \\ 3.5=\frac{k}{-4} \\ k=3.5\times-4 \\ k=-14 \end{gathered}$

So, if it's an inverse variation, the relationship would be

$y=\frac{-14}{x}$

In the second column, x = -2 and y = 7.

Now lets substitute the value of x for -2. If we get y to be 7, then the relationship is an inverse variation

We have

$\begin{gathered} y=\frac{-14}{x} \\ y=\frac{-14}{-2} \\ y=7 \end{gathered}$

Since we got y = 7, the relationship is therefore an inverse variation.

The constant k = -14

The equation for the inverse variation is

$y=\frac{-14}{x}$

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