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 a parabola with points at (-10, 0) and (10, 0) for function analysis.

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 as well as state if we have either a function or not a function. So here we can begin by first identifying if our graph is of a function. And we do this by utilizing the vertical line test. So with the vertical line test, we just simply draw in vertical lines that pass through our graph. And if this vertical line passes through multiple points, then we know we do not have a function. However, noticing with our given graph, we can draw a vertical line at any point on this graph. And we see that we only ever pass through one point. Therefore, we can conclude that we do in fact have a function. And so now we can just move on to identifying our domain and range. So beginning with our domain, we take a look at our X values on our graph. And we see here from our graph that we extend through all X values, we go all the way from negative infinity to positive infinity as indicated by the arrows on the ends of our graph. And we notice that there aren't any other barriers or boundaries on our X values. So we simply go from negative infinity to positive infinity and infinity is always excluded and therefore closed by parentheses. So now we can move on to identifying our range. So for our range, we look at our Y values and we see that our smallest Y value is when Y is equal to zero, we see we have this horizontal line from X is equal to negative to X is equal to positive 10. And so we see that our line or our graph never goes underneath the X axis. Therefore, our Y values are always going to be positive. So for our range, we go from zero to positive infinity. And now here we see that zero is included because we do have part of our graph where Y is equal to zero. So zero is closed by a bracket and then positive infinity is always excluded and therefore closed by a parent C. So we here we have determined that we do in fact have a graph of a function and we have found our domain and range. And so we are left with answer choice D where again we have a function with a domain from negative infinity to positive infinity. And a range from zero 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 of a Relation

Vertical Line Test

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