For each graph, determine whether y is a function of x. Give t...

Question

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

Graph showing two parabolas, one opening upward above y=0 and one opening downward below y=0, on an xy-plane.

Accepted Answer

Hey, everyone here, we are asked to identify if the given graph represents a function. And we are also asked to find its domain and range. Here we have four answer choice options, ABC and D, each of which state the domain and range in interval notation. And they also state whether we have a function or not a function. So here to begin this problem, we can first take a look at our graph and determine if we have a function or not a function. So to do this, we need to utilize the vertical line test. And so for the vertical line test, we simply draw in vertical lines at various points on our given graph. And we see that no matter where we draw this vertical line, the line passes through two different points. And because it passes through more than one point, we know that we do not have a graph of a function. So our graph is not a function. And so now we can move on to determining our domain. So our domain, we need to look at our X values on our graph. And so just following from the left to the right side, we see that there are no limitations on our X values. And so all X values are included. And this tells us that our domain is simply from negative infinity to positive infinity. So now we can take a look at our range by looking at our Y values. And we see starting from the bottom of our graph, we go from negative infinity to the next point or the next Y value which is negative 11. So first we go from negative infinity to negative 11, then we have a gap. And so the next point we go to is 11, positive 11. And then after positive 11, we go all the way to positive infinity. So here we see that both 11 and negative 11 are solid points on our graph. And so both negative 11 and positive 11 are included and closed by brackets and then infinity is always excluded. So both positive and negative infinity get closed by parentheses. So now we have identified our domain and our range and we have also determined that our graph is not of a function. And so we are left with answer choice B where again, we have a function with a domain from negative infinity to positive infinity and a range from negative infinity to negative included and from 11 included to positive infinity. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

Key Concepts

Definition of a Function

Domain and Range

Vertical Line Test

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