Concept explainers
(a)
To sketch: The graph of
(a)
Explanation of Solution
The domain of the given function is
Sketch the graph of given function as shown below.
Figure (1)
Above figure shows the graph of function
(b)
To find: The function
(b)
Answer to Problem 12T
The function
Explanation of Solution
To find whether the function is one-to-one or not, draw a horizontal line on the graph of function if it intersects it at more than one point than it is not one-to-one.
Draw the horizontal line on graph of the given function as shown below.
Figure (2)
Observe from Figure (2) that horizontal line l-l intersects the graph of given function at two points m and p.
Thus, the function is not one-to-one.
(c)
To find: The
(c)
Answer to Problem 12T
Local minimum values are
Explanation of Solution
The graph of given function is shown below.
Figure (3)
Any Point a on any curve is called local maximum when
Any point a on any curve is called local minimum when
Observe from Figure (3) that point a and b are local minimum and point c is local minimum.
Coordinates of point
Thus local minimum values are
(d)
To find: The range of the function
(d)
Answer to Problem 12T
The range of given function in set notation is
Explanation of Solution
The graph of given function is shown below.
Figure (4)
The minimum value of dependent variable as shown in Figure (4) is
So, the range of given function in set notation is
(e)
To find: The intervals on which function is increasing and decreasing.
(e)
Answer to Problem 12T
Function is increasing in interval
Explanation of Solution
The graph of given function is shown below.
Figure (5)
The function is said to be increasing when its graph is rising and function is said to be decreasing when its graph is falling.
Observe from the graph that it is falling in interval
Thus, the function is increasing in
Chapter 2 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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