For each function graphed, give the minimum and maximum values...

Question

For each function graphed, give the minimum and maximum values of ƒ(x) and the x-values at which they occur.

Graph of a function showing a curve with a maximum near x = -3 and a minimum near x = 2 on a grid.

Accepted Answer

Hey, everyone here we are asked to determine the minimum and maximum values of the function shown in the corresponding X values at which the minimum and maximum are found. Here, we are given a graph of a smooth line with two curves that displays our given function. We also have four answer choice options. Answer choice A with a maximum value of four at X is equal to negative four and a minimum value of negative four at X is equal to four. Then answer choice B A maximum value at of four at X is equal to four. Then a minimum value of negative four at X is equal to negative four. Answer choice C A maximum value of six at X is equal to four and a minimum value of negative six at X is equal to negative four. Lastly answer choice D A maximum value of four at X is equal to negative six and a minimum value of negative four at X is equal to six. So to begin solving this problem, we can first start by finding our highest point. So we just want to look for the peak in our graph here. And we see that we have a peak or the highest point at the ordered pair of negative four and four. So with this point, we see that our highest or maximum value, our maximum value is this Y value of the point which is positive four. So we have a maximum value of four. And now the X coordinate tells us the location or the corresponding X value at which the maximum is found. And in this case, that value is negative four. So the maximum value is four at X is equal to negative four. Now we can move on to finding our minimum value. And we do this by looking for the lowest point in our graph and we see that at four and negative four. So now again, we look at the Y coordinate for our value here. So we see our minimum value in this graph is negative four. And now looking at our X coordinate, we see that this minimum value occurs at X is equal to positive four. So now we have determined the maximum value and the corresponding X value for the maximum and minimum values. And so with this, with these solutions, we are left with answer choice. A where we have a maximum value of four at X is equal to negative four and a minimum value of negative four at X is equal to a positive four. Thanks for watching. I hope you found this video helpful and I'll see you again, next time.

For each function graphed, give the minimum and maximum values of ƒ(x) and the x-values at which they occur.

Key Concepts

Maximum and Minimum Values of a Function

Reading and Interpreting Graphs

Function Notation and Evaluation

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