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

Question

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

Accepted Answer

Hello today we're going to be finding the Y intercept for the graph given to us and we're going to be stating its range in set builder notation. So what we are given is this curve starting at 0: and going to 4:00. Now for the Y intercept the Y intercept is the part of the graph that touches the Y axis. And we have one part of the graph that does that, it's the point here at zero comma four. So with that being said, the Y intercept is going to be located at zero comma four or why is equal to four? And notice that this is a solid dot here. That means that this y intercept is going to be included in the range of the graph. So just to quickly state the Y intercept is going to be equal to four. Now let's go ahead and find the range of the graph. The range of the graph focuses on the lowest possible value for Y going to the highest possible value for Y. So we're going to be reading this graph, going from the bottom up. So let's go ahead and take a look at the lowest point of the graph which is going to be here at 4:00. Now, at this point here, why is equal to zero? However, this point is represented with an open dot which means that this value of Y is not included within the range. So that means that the values for why have to be greater than zero but is greater than and not greater than or equal to because why cannot be equal to zero. Now let's go ahead and take a look at the highest point of the graph. Again, the highest point is going to be here at zero comma four. And we know that the y value at this point is going to be y is equal to four. Now we can go ahead and include this value in the range because the dot here is represented with a solid dot. So that means that any value of y at this point, why has to be less than or equal to four. Now, let's just go ahead and put this together in the set builder notation. So we first start by writing a bracket and saying that why? Such that and we want to go ahead and combine these two arguments together, combining these two arguments is going to give us y is greater than zero but less than or equal to four. And we go ahead and close that and that's going to be the range of the given graph. So just to reiterate, we have a y intercept at Y is equal to four and all the possible values of why lie between zero and four and include the value of four, but don't include zero. So the range is going to be Y such that Y is greater than zero but less than or equal to four. And with that being said, the answer to this problem is going to be a So I hope this video helps you in understanding how to find the range of a graph, 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 range; b. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

Key Concepts

Function Range

Y-Intercept

Interpreting Open and Closed Points on Graphs

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