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 showing a piecewise function with a line segment and a horizontal line, missing values at x = -4 and x = 4.

Accepted Answer

Hello. Today we're going to be identifying the domain and range of the given function. So what we are given is the graph of a function whose left most point is a solid dot. And the right most point is an open dot. So let's go ahead and start by identifying the domain. The domain focuses on the lowest possible value for X. And the highest possible value for X on the graph. So we're gonna be reading this graph going from left to right. The left most point is located at negative eight on the X axis. So that means that the lowest possible value for X is going to be a negative eight. And since the dot at this point is solid, that means we're going to be including negative eight in our domain. Now let's go ahead and focus on the right most point of X. The right most point is going to be where X is equal to 10. But keep in mind that there is a hole in the graph at X is equal to 10. So we're not going to be including the value of 10 in our domain. So let's go ahead and write this interval notation. So we're going to start by listing our lowest possible value for X, which is negative eight. And we're going to assign negative eight a bracket because we're including negative eight in our domain. Then we're going to put AO and put our highest possible value for X, which is going to be 10. However, we're not going to be including 10 in our domain. So we're going to assign it a parentheses. And this is going to be the domain for the given function. Now let's go ahead and identify the range. Now the range focuses on the lowest possible value for Y and the highest possible value for Y. So we're going to be reading this graph, going from the bottom to the top. So let's go ahead and take a look at the lowest possible value for Y. Which is going to be at y is equal to negative 10. Now keep in mind that the corresponding coordinate and y is equal to negative 10 is an open hole on the graph. So we're not going to be including the value of negative 10 in our range. Now the highest possible value for Y is going to be eight. So why is going to equal to eight at the highest point of the graph? And since the highest point is a solid dot, we're going to be including eight in our range. So again, in order to list the range, we're gonna start by listing the lowest possible value for Y, which is negative 10. But since we're not including this value, we're going to assign negative 10 of parentheses. And after the comma we're going to put the highest possible value for y, which in this case is eight. And since we're including eight in our range, we're going to assign it a bracket and this is going to be the range in interval notation. So just to summarize, the domain is from negative 8 to 10, not including 10, and the range is from negative 10 to 8, not including negative 10. 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 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 and Function Values

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