In Exercises 11–26, determine whether each equation defines y as ...

Question

In Exercises 11–26, determine whether each equation defines y as a function of x. |x|- y = 5

Accepted Answer

Hello. Today we're going to determine whether the given function is a function of Y. In terms of X. So the function given to us is the absolute value of nine X minus three Y. Is equal to six. Now, in order to determine whether this is a function of Y. In terms of X. We need to go ahead and sulfur Y for first. In order to do that, we're going to add three Y to both sides of the equation And we're going to subtract 6 to both sides of the equation. Doing so is going to give me three. Y is equal to the absolute value of nine X minus six. And in order to solve for y, I'm gonna divide everything by three. So y is equal to the absolute value of nine X minus 6/3. And for one more simplification, I can go ahead and separate this into two separate fractions. So what we get is the absolute value of nine X over three minus 6/3 and 6/3 is going to reduce to two. So why is equal to the absolute value of nine X over three minus two. Now this is the graph of an absolute value function. And this is gonna be the rough graph where we have an absolute value function with the origin at 0:00 -2. And it opens up positively. And so one way to determine whether this is a function or not, is to perform the vertical line test on this function. So as long as I intersect this line at any given point and the line touches the graph at exactly one point at any given time. This is a function of why. In terms of X, and this graph passes the vertical line test, so this is a function of why in terms of X. Therefore the solution to this problem is going to be a So I hope this video helps you in determining this, and I'll go ahead and see you all in the next video.

Struggling with College Algebra?

In Exercises 11–26, determine whether each equation defines y as a function of x. |x|- y = 5

Watch next

Two-Variable Equations practice set