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 piecewise curve with points at (0,0), (3,4), and a vertical segment, illustrating domain and range.

Accepted Answer

Hey, everyone here, we are asked to identify if the given graph represents a function. And we also need to find the domain and range. Here we have four answer choice options where answer choices A and C state that we do not have a function. However, answers B and D state that we do have a function and all answer choice options have differing domains and ranges. So to begin this problem, we want to start by identifying if our given graph does in fact represent a function. So to do this, we need to utilize the vertical line test where we simply draw vertical lines at various points on our given graph to make sure that these lines only pass through one point. However, we see here that at X is equal to 30 that our vertical line test fails since we pass through multiple points. And since the vertical line test fails, this confirms that we do not have a graph of a function. So since we have determined that we do not have a function, we can now move on to the second part where we need to find the domain and range starting with the domain. If we recall the domain are all of our X values for which our graph spans to. So we can see that at the left of our graph that we have this arrow pointing to the left. And this tells us that we go to next negative infinity along the X axis. And now looking at the top right of our graph, we see another area pointing perfectly horizontally to the right. So this tells us that we also go to positive infinity. And since we go from negative infinity to positive infinity infinities get closed by parentheses since they are never included. So we have found our domain of our graph. And now we just need to determine the range. And if we recall the range are all of our Y values. And so at an initial glance, we see that our range appears to be from negative to the top here, which is 30. So it seems to go from negative 10 to 30. However, we can notice again to the left of our graph that we have this arrow arrow pointing to the left at an angle. So this tells us that we actually go to a positive infinity along the Y axis. So our range is from negative 10, the bottom of the graph here. And then following the arrow, we go to positive infinity here, negative 10 gets closed by a bracket. So it is included as a point on our graph. And then we go to positive infinity where infinity is always closed by a parentheses. So now we have found our domain and range and also determined that we do not have a graph of a function. Therefore, we are left here with answer choice C where again, we do not have a function and our domain is from negative infinity to positive infinity. And our range is from negative 10 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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