Question Video: Finding the Range of an Absolute Value Function from the Graph | Nagwa Question Video: Finding the Range of an Absolute Value Function from the Graph | Nagwa

# Question Video: Finding the Range of an Absolute Value Function from the Graph Mathematics

Find the range of the function ๐(๐ฅ) = |โ2๐ฅ โ 2|.

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### Video Transcript

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

Now, weโve actually been given the graph of this function of the absolute value of negative two ๐ฅ minus two. And thatโs 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. Itโs the complete set of all possible resulting values of the dependent variable โ thatโs often ๐ฆ, but here weโre calling it ๐ of ๐ฅ โ after weโve substituted the domain. Now, the domain of an absolute value function is simply all real values of ๐ฅ.

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