
Concept explainers
To analyze: the given polynomial function

Answer to Problem 13RE
Explanation of Solution
Given:
Calculation:
Let us consider the following polynomial function,
Analyse the graph of the given function.
For this follow the following steps:
Step 1:Determination of the end behaviour of the graph of the function.
The end behaviour of the graph of a function is similar to the leading term of the function. So, first of all determine the degree of the function.
So,
Here, the degree of the polynomial is 3. So, the graph off behaves like
Step 2:
Graph the function using a graphing utility.
Plot the given function.
Step 3: Next, approximate the x and the y intercepts of the graph.
From the graph, the graph passes through y -axis at a single point, so the y -intercept is at
Also, the graph intersects the x -axis at 1point,
Step 4:
Create a table to find points on the graph around each x intercept.
Here, for
Step 5:
Approximate the turning points of the graph.
From the graph off , f has two turning points.
Using MAXIMUM, one turning point is at
Step 6:
Complete the graph using all the above information.
Step 7:
Determine the range and domain of the function.
Domain and range of the function are the set of all real numbers. So,
Step 8:
Determine where the function is increasing and where it is decreasing.
From the graph, the function is increasing in the interval
Conclusion:
Therefore, the polynomial function
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