Question Video: Properties of Reciprocal Functions

Video Transcript

The figure shows the graph of 𝑦 equals one divided by 𝑥. Write down the two asymptotes of 𝑦 equals one divided by 𝑥. What is the domain of the function? What is the range of the function?

Asymptotes will be lines that the graph approaches but never touches, which can be found here at 𝑥 equals zero and here at 𝑦 equals zero. Again, these are lines that the graph approaches but never actually touches.

And if we think about the equation itself, 𝑦 equals one divided by 𝑥, if we would plug in zero for 𝑥, one divided by zero is undefined. It cannot happen. So 𝑥 cannot be zero, which is why the graph never actually touches that.

And then if we would switch it, if we would make 𝑦 be zero, one divided by what gives us zero? You can’t take one and divide it by any number at all and get zero. It’s not possible. So 𝑦 cannot be zero.

Next we want to know what is the domain of the function. These are all of the values that 𝑥 can take on. Well, looking at our graph, any number for 𝑥 will work except for one. 𝑥 cannot be zero. Therefore, 𝑥 is in the real numbers, except 𝑥 cannot be zero.

And next we need to find what is the range of the function. And the range deal with the values for 𝑦. And any value of 𝑦 will work except for 𝑦 equals zero. Therefore, 𝑦 is in the real numbers, except 𝑦 cannot be zero. So these will be our final answers.