Question

Determine the domain and range of the original function Express your answer in interval notation.

Answer 1

Hello!

We have the following function:

$p(x)=(x-3)^3$

For the domain (x-axis), we have to check if there is any value that makes this function impossible to solve.

As it hasn't a fraction, it admits any value for x.

So, the domain is:

$\left(-\infty \:,\:\infty \:\right)$

Now let's talk about the range (y-axis):

As it has exponent 3, it admits all values (positive and negative), without restrictions.

So, the range is:

$\left(-\infty \:,\:\infty \:\right)$

Answer:

Domain:

$\left(-\infty \:,\:\infty \:\right)$

Range:

$\left(-\infty \:,\:\infty \:\right)$