Determine whether each relation defines a function, and give t...

Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1 – 4.

Accepted Answer

Welcome back. I am so glad you're here. We are asked to identify if the given relation represents a function, then determine its domain and range. Then we have a graph. It has a vertical Y axis, a horizontal X axis. And across the graph we have a blue curved line. Our answer choices are answer choice. A not a function domain of open bracket, negative 4 to 5 close bracket. And a range from open parentheses, negative infinity to infinity, closed parentheses. Answer choice B not a function domain from open parentheses, negative infinity to positive infinity, closed parentheses. And a range from open bracket negative 4 to close bracket. Answer choice C function with a domain from open parentheses, negative infinity to positive infinity, close parentheses. And a range from open parentheses, negative infinity to positive infinity and answer choice D function with a domain of open parentheses, negative infinity to infinity, closed parentheses. And a range of open bracket negative four to positive five close bracket. All right. So we are supposed to first figure out if this is a function or not. And we recall from previous lessons that when we're looking at a graph and we want to determine if it's a function, we can use the vertical line test. And with the vertical line test, we're going to draw vertical lines up and down. And if our vertical, straight up and down lines touch our graph line, in this case, the blue line more than once at any point, then it is not a function. So this would not be a function if it touches our line more than one time. But if we draw our vertical lines anywhere and it only touches it once, then yes, this would be a function. So let's try drawing some vertical lines here. We've only touched the graph once another vertical line only touches the graph. Once anywhere, we try to draw a vertical line, we are only touching the graph, the blue line one time. So this is a function. Yes. Now we need to determine the domain and the range, the domain is all of the possible X values. The X values are the horizontal values. And we see here that at the beginning and the end of our graph, there are arrows meaning that this continues forever. And so even though it looks like it's mostly going up and mostly going down at the ends of our graph, it is slowly continuing to the left for forever toward negative infinity and slowly continuing to the right four forever to positive infinity. So our domain is from negative infinity to positive infinity. And we open and close that with parentheses, open parentheses, negative infinity, comma infinity, closed parentheses because we'll never quite obtain infinity. And parentheses indicate that those are not included. We can't actually get to infinity. Now, the range is all of the possible Y values. Those are the vertical ones going up and down. And again, we have those arrows and those arrows are continuing from negative infinity to positive infinity. So the range is again open parentheses, negative infinity, comma infinity, closed parentheses. We look at our answer choices and this matches with answer choice. C well done. We'll catch you on the next one.

Determine whether each relation defines a function, and give the domain and range. See Examples 1 – 4.

Key Concepts

Definition of a Function

Domain of a Relation

Range of a Relation

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