In Exercises 77–92, use the graph to determine a. the function's ...

Question

In Exercises 77–92, use the graph to determine a. the function's domain; b.the x-intercepts, if any; and e. the missing function values, indicated by question marks, below each graph.

Graph showing a curve with points (0,4) and (4,0) marked.

Graph of a V-shaped function with question marks for f(-4) and f(3).

Accepted Answer

Hello. Today we're going to be finding the X intercept for the given graph. And we're going to state its domain in set builder notation. So we have this curve given to us And the curve starts at 0: and makes its way down 24 comma zero. Now let's go ahead and first determine whether there is an X intercept or not. If there is an X intercept, the graph would lie directly on the X axis and there is one point that is directly on the X axis, it is four comma zero. However, this point is represented with an open circle mean that there is a whole of the graph on the X axis. Since there is a hole in the graph of the X axis, that means that the domain is not including the value for comma zero. And since the value for comma zero is not included, that means that there is no x intercept of the graph. So that's the first portion of the question. Now the second portion is to go ahead and state the domain and set builder notation. So let's go ahead and do that for the domain. We are looking for the lowest possible X value of the graph to the highest possible X value. So we're going to be reading this graph going from left to right. The lowest possible point on the graph is at zero, comma four. As this is the left most point of the graph. That means that the lowest possible value of X is going to be zero and we're including that value of zero. Since this point is represented with a dotted line. So that means that X is greater than or equal to zero. And if we make our way to the right, the right most point is given to us as four comma zero. But once again we're not including this value of four in the domain. So that means that X has to be less than four. So the possible values of X for the graph is X is greater than or equal to zero, but less than four. Not including four. Now we want to go ahead and put this in set builder notation. Set builder notation. We first start by writing a bracket and we're going to write the statement X. Such that. Now we put the statement that describes all the values of X in the graph and we wrote that right here. So we have X. Such that X is less than or greater than or equal to zero and less than four. And we're gonna close that with the bracket and this is going to be the domain of the graph in set builder notation. And with that being said, the answer to this problem is going to be C. So I hope this video helps you in understanding how to determine the domain and whether there is an X intercept or not. And I'll go ahead and see you all in the next video

In Exercises 77–92, use the graph to determine a. the function's domain; b.the x-intercepts, if any; and e. the missing function values, indicated by question marks, below each graph.

Key Concepts

Domain of a Function

X-Intercepts

Function Values

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