### Video Transcript

Find the range of the function π of π₯ is equal to the absolute value of negative two π₯ minus two.

Now, weβve actually been given the graph of this function of the absolute value of negative two π₯ minus two. And thatβs 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. Itβs the complete set of all possible resulting values of the dependent variable β thatβs often π¦, but here weβre calling it π of π₯ β after weβve substituted the domain. Now, the domain of an absolute value function is simply all real values of π₯.

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