Question

Use the drawing tools to form the correct answers on the grid.

Answer 1

Answer:

The function $f(x)= \frac{1}{x^2+2}$ is continuous for all real numbers

Step-by-step explanation:

To know the possible points of discontinuity of this function, we must find out when the denominator of the function is equal to 0.

The denominator is:

$x ^ 2 + 2$

Then we equal 0 and clear x

$x ^ 2 +2 = 0\\\\x ^ 2 = -2$

$x ^ 2> 0$ for any real number.

This means that

$x ^ 2 +2> 0$ for all reals numbers.

Therefore, the function $f(x)= \frac{1}{x^2+2}$ is continuous for all real numbers, that is, it does not have discontinuities.

The graphic of this function is shown in the image