### Video Transcript

Find the range of the function ๐ of ๐ฅ is equal to the absolute value of negative two ๐ฅ minus two.

Now, weโve actually been given the graph of this function of the absolute value of negative two ๐ฅ minus two. And thatโs really helpful because we can find the range of a function from its graph. Now, we begin by recalling what we mean by the range of a function. Itโs the complete set of all possible resulting values of the dependent variable โ thatโs often ๐ฆ, but here weโre calling it ๐ of ๐ฅ โ after weโve substituted the domain. Now, the domain of an absolute value function is simply all real values of ๐ฅ.

We see when we substitute in all real values of ๐ฅ to our function, we get the graph shown. In this case, we see the smallest resulting value of ๐ฆ is zero. The arrows show us that the values of ๐ฆ continue to grow up to positive โ. We can say then that for the function ๐ฆ is equal to the absolute value of negative two ๐ฅ minus two, ๐ฆ must be greater than or equal to zero and less than โ. And so we found the range of our function. Itโs greater than or equal to zero and less than โ.