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
PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
- Number 4 plsarrow_forwardGood Day, Would appreciate any assistance with this query. Regards,arrow_forwardThis question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. A B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3t) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot(3πt) sin(3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411- 4 -2 sin (3лt) (d)…arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





