Video: Representing a Given Function in a Table

Video Transcript

Which of the following is a table of values for the function 𝑦 equals seven 𝑥 minus three?

Our function is 𝑦 equals seven 𝑥 minus three. And all of the tables have 𝑥 values of zero, one, two, and three. We have to find the 𝑦-values for each of these 𝑥-values. And we do that by taking the 𝑥-values from the table and plugging them into the equation.

Here we’ve substituted zero for 𝑥. Seven times zero equals zero. Zero minus three equals negative three. When our 𝑥-value is zero, the 𝑦-value is negative three. We’re going to repeat the same process, substituting a one for our 𝑥. Seven times one equals seven. Bring down the minus three. Seven minus three is four. And that means when 𝑥 equals one, 𝑦 equals four.

And now we’ll substitute the two for our 𝑥-value. Seven times two equals 14. 14 minus three equals 11. Whenever 𝑥 is two, 𝑦 will be equal to 11. And now our final 𝑥-value, 𝑥 equals three. We now have 𝑥 times three minus three. Seven times three equals 21. 21 minus three equals 18. When 𝑥 equals three, 𝑦 equals 18.

We need to look for the table whose corresponding 𝑥- and 𝑦-values look like the numbers we found. Table a has a wrong value for 𝑥 equals two. Table c has a wrong value for 𝑥 equals one. Table d has a wrong value where 𝑥 equals zero. And table e has a wrong value for 𝑥 equal three. Only table b has correct corresponding 𝑥- and 𝑦-values for the function 𝑦 equals seven 𝑥 minus three.