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 𝑓(𝑥) = |−2𝑥 − 2|.

01:12

Video Transcript

Find the range of the function 𝑓 of 𝑥 is equal to the absolute value of negative two 𝑥 minus two.

Now, we’ve actually been given the graph of this function of the absolute value of negative two 𝑥 minus two. And that’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. It’s the complete set of all possible resulting values of the dependent variable — that’s often 𝑦, but here we’re calling it 𝑓 of 𝑥 — after we’ve substituted the domain. Now, the domain of an absolute value function is simply all real values of 𝑥.

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

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