Concept explainers
a.
To calculate: the x -coordinate of every turning point and also determine whether the coordinates are
a.
Answer to Problem 51STP
Explanation of Solution
Given information:
Formula used:
Relative maximum- The point on the graph is a relative maximum of the function when there is no other nearby points that have greater y -coordinate.
Relative minimum- The point on the graph is a relative minimum of the function when there is no other nearby points that have lesser y -coordinate.
Calculation:
According to the graph ,
We observed three turning points
At point
At point
At point
Hence, the following are the x -coordinate
b.
To calculate: the x -coordinate of every zero.
b.
Answer to Problem 51STP
The x -coordinate of every zero are
Explanation of Solution
Given information:
Formula used:
The changes in sign indicate that there are zeros between those two x -values.
Calculations:
According to the graph ,
We observed three turning points
The graph crosses the x -axis at two points.
At
Hence, the x -coordinate of every zero are
c.
To calculate: the smallest possible degree of the function.
c.
Answer to Problem 51STP
Smallest degree of the function is 4.
Explanation of Solution
Given information:
Formula used:
The maximum and minimum values of a function are called extrema .
These points are referred to as turning points.
The graph of the polynomial function of degree n has at most
Calculation:
According to the graph ,
We observed three turning points at which the function changes.
Hence, the smallest possible degree of the function is 4.
d.
To calculate: the domain and range of the function .
d.
Answer to Problem 51STP
The domain and range of the function are all real numbers and
Explanation of Solution
Given information:
Formula used:
Domain of the function : is the set of all values for which function is defined.
Range of the function : is the set of all values that f takes.
Calculation:
According to the graph ,
Domain is presented by x -axis. This implies domain is all real numbers.
Range is presented by y -axis. This implies
Hence, the domain and range of the function are all real numbers and
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