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=-6x+4

Accepted Answer

Hey, everyone in this problem, we're asked to find out if the given equation represents a function. And also to find the domain in range. The equation we're given is three Y is equal to negative X plus one. We're given four answer choices. And we're gonna come back to those as we work through this problem. Now, three Y is equal to negative 171 X plus one. And the first thing I want you to notice is that this is the equation of a lot and we have Y with an exponent one, we have an X term with an exponent one and we have a constant term and these are added to get OK. So this is the equation of a line. If you were to divide the left and right hand sides by three, this would be in standard form and Y is equal to something multiplied by X plus something. So we expect that this is gonna be a function because we know that a line is a function. But let's think about this in detail for a function. We want to think about every X value OK. For every X value we substitute in what do we get for our eyes? OK. Well, if we were to substitute an X value in here, we multiply it by negative 171. That's gonna give us one, a one answer, we add one and then we're gonna divide by three. So for every X value, we're only going to get one corresponding Y value. And what that tells us is that this is a function. And you can think about this graphically and sometimes students are more comfortable with that. So if you think about having the graph of a function, you would or the graph of an equation that you're trying to determine if it's a function, you would wanna do your vertical line test. So if you draw a vertical line, OK, that's one particular X value. And you want to make sure that the equation passes through that vertical line only once. And what that indicates is that there's only one Y value associated with that X value where you drew your vertical line A and in this case, it would pass that vertical line test just like it passes this test when we do it algebraically. All right. So we know this is a function, we can eliminate options A and B because they say that this is not a function. And now we're left with option C and D and to find the domain in range. Now we just said that this is the equation of a line. OK. Equation of a line. We know we can have the domain and range from negative infinity to positive infinity and any X value we can substitute in and we get the all possible Y values as well. And so our domain is gonna be from negative infinity to positive infinity. And our range as well will be from negative infinity to positive infinity. There are no restrictions in this case. And so the correct answer choice is gonna be option D A, this represents a function and the domain and range are both from negative infinity to positive infinity. That's it for this one. Thanks everyone for watching. I hope this video helped.

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y=-6x+4

Key Concepts

Function Definition

Domain and Range

Linear Functions

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