Video Transcript
Write the relation 𝑅 for the following arrow diagram.
First of all, we can just write that 𝑅 will be equal to some set. In order to figure out the relationship pairs from the arrow diagram, we need to consider where each arrow begins. We have a starting point at zero, a starting point at negative eight, a starting point at negative nine, and we also have a starting point at eight and nine. It’s worth pointing out that these starting points represent the inputs in a relation. Based on this, we can say that there will be five relationships.
Starting back at zero, if we start with a zero, the result will be zero. This is because the end of the arrow that begins at zero ends at zero. Using the same logic, the arrow that begins at negative eight ends at positive eight, which means we have the relationship negative eight, eight. When we begin at negative nine, we end at positive nine. So we have negative nine, nine. Now we need to go back and consider if we start at positive eight, we end at negative eight for the coordinate eight, negative eight. And finally, when we start at positive nine, we end at negative nine.
All of these endings represent the outputs. And when we’re writing these relationships in coordinate form, the input, the starting point, is the 𝑋-value and the output, the ending point, is the 𝑌-value. The relation 𝑅 is the set zero, zero; negative eight, eight; negative nine, nine; eight, negative eight; and nine, negative nine.
