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 domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

Graph of a function increasing from (-2,1) through (0,1) to (5,3) with missing value f(3) indicated.

Accepted Answer

Hello. Today we're going to be identifying the domain and range of the given graph below. So the graph given to us is this curve that has a hole at the origin And has the last point at 5: with a solid dot at the end of the curve. So let's go ahead and identify the domain. The domain focuses on the lowest possible value for X and the highest possible value for X. So we're going to be reading this graph from left to right in order to identify the domain. So the left most point of the graph or the left most X value of the graph is going to be zero. But keep in mind that there is a hole at the origin of the graph. So that being said the domain or the lowest possible value for X is going to be zero. But we're not including it in our domain. Now let's take a look at the highest possible value for X. Since the graph ends at 5:07, the highest possible value for X is going to be five. So we're going to have X is equal to five. But since the graph ends in a solid dot, we're going to be including five in our domain. So the way that we write this interval notation, we're going to start with the parentheses E and zero. This means that the lowest possible value for X is going to be zero. But we're not including zero in our domain. And finally we're going to put five after the comma and ended with the bracket. And this indicates that the highest possible value for X is five and we're including five in the graph. And this is going to be the domain for the graph. Now let's identify the range of the graph. The range focuses on the lowest possible value for Y and the highest possible value for Y. So we're going to be reading the graph from the bottom, going to the top. So the lowest possible value for y is going to be zero. But again, there's a hole at the origin of the graph. So the lowest possible value for Y is going to be zero, but we're not including it in our range. Now, the highest possible value for Y is going to be seven because the last point of the graph ends at five comma seven, but the corresponding y value is going to be seven and we're going to include the value of seven in our range because the last point is a solid dot. So the way that we write this interval notation, once again, we're going to start with the parentheses E and put zero before the comma. Because this is saying that the lowest possible value for the range is zero, but we're not including it in the range. And we're going to put a seven after the comma and end it with the bracket because this is saying that the highest possible value for y is seven and it is included in our range. And this is going to be the range for the given graph. So just to summarize, the domain is going to be from 0 to 5, not including zero, and the range is going to be from 0 to 7, not including zero. With that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem, 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 function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

Key Concepts

Domain of a Function

Range of a Function

Intercepts of a Function

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