Concept explainers
a.
To determine which among the twelve basic functions does not have the property
The basic functions that do not process the property that
- The reciprocal function,
- The exponential function,
- The natural logarithm function,
- The cosine function
- The logistic function
Concept Used:
The twelve basic functions:
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
Calculation:
Any function
Now, observe the graphs of the basic functions:
The graphs of the reciprocal function, the exponential function, the natural logarithm function, the cosine function and the logistic function seem to be not passing through the origin.
Thus, the basic functions that do not process the property that
- The reciprocal function,
- The exponential function,
- The natural logarithm function,
- The cosine function
- The logistic function
Conclusion:
The basic functions that do not possess the property that
- The reciprocal function,
- The exponential function,
- The natural logarithm function,
- The cosine function
- The logistic function
b.
To determine which one among the basic functions possesses the property that
The identity function
Given:
It is given that only one basic function possesses the property that
Calculation:
Observe the identity function
Thus, the identity function possesses the property.
Since it is given that only one among the basic functions possesses this property, only the identity function possesses this property.
Conclusion:
The identity function
c.
To determine which one among the basic functions possesses the property that
The exponential function
Given:
It is given that only one basic function possesses the property that
Calculation:
Observe the exponential function
Thus, the exponential function possesses the property.
Since it is given that only one among the basic functions possesses this property, only the exponential function possesses this property.
Conclusion:
The exponential function
d.
To determine which one among the basic functions possesses the property that
The logarithmic function
Given:
It is given that only one basic function possesses the property that
Calculation:
Observe the logarithmic function
Thus, the logarithmic function possesses the property.
Since it is given that only one among the basic functions possesses this property, only the logarithmic function possesses this property.
Conclusion:
The logarithmic function
e.
To determine which four among the basic functions possess the property that
The basic functions possessing the property that
- The identity function
- The cubing function
- The reciprocal function
- The sine function
Given:
Given that four among the basic function possess the property that
Concept Used:
Any function showing the property that
Now, if a function is odd, its graph will be symmetrical about the origin.
Calculation:
Observe the graphs of the basic functions:
The identity function, the cubing function, the reciprocal function and the sine function are the only ones whose graphs are symmetric about the origin.
Thus, the basic functions possessing the property that
- The identity function
- The cubing function
- The reciprocal function
- The sine function
Conclusion:
The basic functions possessing the property that
- The identity function
- The cubing function
- The reciprocal function
- The sine function
Chapter 1 Solutions
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