Determine whether each relation defines y as a function of x. Giv...

Question

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5.

y = 2x - 5

Accepted Answer

Hello, today we're going to be determining whether the relation between X and Y is a function or not, then we're going to be determining the domain and range. So the relation given to us is Y is equal to nine X minus 17. Now, the relation roughly matches the shape or the equation of a line. The equation of a line in slope intercept form is Y is equal to MX plus B. This is where the constant B is the Y intercept or the starting point of the line. And M represents the slope of the line. In this case here, Y equal to nine, X minus 17. B will equal to negative 17 and M will equal to positive nine. So if you were to graph the equation of the line, the line will start at the Y value negative 17. And since we have a slope of nine, the X intercept is going to be at 9/17. And if we draw a line between the two points, we get the equation of a positive line. Now, in order to determine whether this is a function or not, we're going to use the vertical line test. So we're going to draw some vertical lines cutting across the graph. And as long as the vertical lines intercept the graph at exactly one point that will show that the relation is a function. If we take a look at the first vertical line, the vertical line intercepts the line at exactly one point. The same can be said for the second vertical line and the third vertical line. So that means the equation passes the vertical line test. Therefore, Y is equal to nine X minus 17 is a function. Now that we've determined that the relation is a function we're going to start by finding the domain of the function. Now, Y equal to nine X minus 17 is in the form of a polynomial. And the domain for any polynomial will be negative infinity to positive infinity. Then we'll need to find the range for the given function. Now the range focuses on the lowest Y value to the highest Y value as the value of X decreases, the values of Y are going to decrease along with X to negative infinity. And as X increases to positive infinity, the value of Y will increase to positive infinity. What this means is that the domain is going to be from negative infinity to positive infinity. And these will be the values for the domain and range. So just to summarize, we use the vertical light test to determine that Y is equal to nine X minus is a function. The domain is from negative infinity to positive infinity. And the range is also from negative infinity to positive infinity. With that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y = 2x - 5

Key Concepts

Function Definition

Domain

Range

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