Calculus: Graphical, Numerical, Algebraic, 3rd Edition Answers Ch 1 Prerequisites for Calculus Ex 1.2
Calculus: Graphical, Numerical, Algebraic Answers
Chapter 1 Prerequisites for Calculus Exercise 1.2 1E
Chapter 1 Prerequisites for Calculus Exercise 1.2 1QR
Solving for x means we simply rearrange the equation and take the terms with x to the left hand side.
Given equation is
Chapter 1 Prerequisites for Calculus Exercise 1.2 2E
Consider an equilateral triangle
(a) Let n represent height and s represent side length.
Using the Pythagoras theorem, we get,
Chapter 1 Prerequisites for Calculus Exercise 1.2 2QR
Chapter 1 Prerequisites for Calculus Exercise 1.2 3E
Chapter 1 Prerequisites for Calculus Exercise 1.2 3QR
Chapter 1 Prerequisites for Calculus Exercise 1.2 4E
Chapter 1 Prerequisites for Calculus Exercise 1.2 4QR
Chapter 1 Prerequisites for Calculus Exercise 1.2 5E
(b) The graph of the given function will be:
[-5, 5] by [-10, 10]
Chapter 1 Prerequisites for Calculus Exercise 1.2 5QR
Chapter 1 Prerequisites for Calculus Exercise 1.2 6E
Chapter 1 Prerequisites for Calculus Exercise 1.2 6QR
Chapter 1 Prerequisites for Calculus Exercise 1.2 7E
(b) The graph of the given function will be:
[-3, 10] by [-3, 10]
Chapter 1 Prerequisites for Calculus Exercise 1.2 7QR
Chapter 1 Prerequisites for Calculus Exercise 1.2 8E
(b) The graph of the given function will be:
[-10, 3] by [-4, 2]
Chapter 1 Prerequisites for Calculus Exercise 1.2 8QR
Chapter 1 Prerequisites for Calculus Exercise 1.2 9E
(b) The graph of the given function will be:
[-4.7, 4.7] by [-6, 6]
Chapter 1 Prerequisites for Calculus Exercise 1.2 9QR
Chapter 1 Prerequisites for Calculus Exercise 1.2 10E
(b) The graph of the given function will be:
[-10, 3] by [-1, 2]
Chapter 1 Prerequisites for Calculus Exercise 1.2 10QR
Chapter 1 Prerequisites for Calculus Exercise 1.2 11E
(b) The graph of the given function will be:
[-4, 4] by [-4, 4]
Chapter 1 Prerequisites for Calculus Exercise 1.2 11QR
Chapter 1 Prerequisites for Calculus Exercise 1.2 12E
Chapter 1 Prerequisites for Calculus Exercise 1.2 12QR
Chapter 1 Prerequisites for Calculus Exercise 1.2 13E
Chapter 1 Prerequisites for Calculus Exercise 1.2 14E
(b) The graph of the given function will be:
[-4.7, 4.7] by [-6, 6]
Chapter 1 Prerequisites for Calculus Exercise 1.2 15E
(b) The graph of the given function will be:
[-6, 6] by [-3, 3]
Chapter 1 Prerequisites for Calculus Exercise 1.2 16E
(b) The graph of the given function will be:
[-4.7, 4.7] by [-2, 4]
Chapter 1 Prerequisites for Calculus Exercise 1.2 17E
(b) The graph of the given function will be:
[-4.7, 4.7] by [-3.1, 3.1]
Chapter 1 Prerequisites for Calculus Exercise 1.2 18E
(b) The graph of the given function will be:
[-4.7, 4.7] by [-1, 5]
Chapter 1 Prerequisites for Calculus Exercise 1.2 19E
(b) The graph of the given function will be:
[-6, 6] by [-3, 3]
Chapter 1 Prerequisites for Calculus Exercise 1.2 20E
(b) The graph of the given function will be:
[-4.7, 4.7] by [-3.1, 3.1]
Chapter 1 Prerequisites for Calculus Exercise 1.2 21E
We know that a function,
f(x) is said to be even if it fulfills the following criteria:
f(-x) = f(x)
f(x) is said to be odd if it fulfills the following criteria:
f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.2 22E
We know that a function,
f(x) is said to be even if it fulfills the following criteria:
f(-x) = f(x)
f(x) is said to be odd if it fulfills the following criteria:
f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.2 23E
We know that a function,
f(x) is said to be even if it fulfills the following criteria:
f(-x) = f(x)
f(x) is said to be odd if it fulfills the following criteria:
f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.2 24E
We know that a function,
f(x) is said to be even if it fulfills the following criteria:
f(-x) = f(x)
f(x) is said to be odd if it fulfills the following criteria:
f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.2 25E
We know that a function,
f(x) is said to be even if it fulfills the following criteria:
f(-x) = f(x)
f(x) is said to be odd if it fulfills the following criteria:
f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.2 26E
We know that a function,
f(x) is said to be even if it fulfills the following criteria:
f(-x) = f(x)
f(x) is said to be odd if it fulfills the following criteria:
f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.2 27E
We know that a function,
f(x) is said to be even if it fulfills the following criteria:
f(-x) = f(x)
f(x) is said to be odd if it fulfills the following criteria:
f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.2 28E
We know that a function,
f(x) is said to be even if it fulfills the following criteria:
f(-x) = f(x)
f(x) is said to be odd if it fulfills the following criteria:
f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.2 29E
We know that a function,
f(x) is said to be even if it fulfills the following criteria:
f(-x) = f(x)
f(x) is said to be odd if it fulfills the following criteria:
f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.2 30E
We know that a function,
f(x) is said to be even if it fulfills the following criteria:
f(-x) = f(x)
f(x) is said to be odd if it fulfills the following criteria:
f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.2 31E
[-4.7,4.7] by [-1,6]
The domain will be (-∞,∞)
The range is [2,∞)
Chapter 1 Prerequisites for Calculus Exercise 1.2 32E
[-4,4] by [-2,3]
Chapter 1 Prerequisites for Calculus Exercise 1.2 33E
[-3.7,5.7] by [-4,9]
Chapter 1 Prerequisites for Calculus Exercise 1.2 34E
[-2.35,2.35] by [-1,3]
Chapter 1 Prerequisites for Calculus Exercise 1.2 35E
According to the vertical line test:
If every vertical line in the x- y plane intersects a given curve at most one point, then the curve is the graph of a function.
This is true because it the vertical line holds, then tor each x-coordinate there is at most one y-coordinate giving a point on the curve. This y-coordinate would correspond to the value assigned to the x-coordinate.
Since there is only one y-coordinate, the assignment would be unique.
This satisfies the definition of a function which states that a function to be in existence, it is required that each element in the domain has a unique element in the range.
Chapter 1 Prerequisites for Calculus Exercise 1.2 36E
As given in the question, for a function to be symmetric about x-axis, the point (x, y) must lie on the curve it and only it the point (x, -y) on the curve.
Drawing a vertical line through a symmetric curve:
The curve in case y=0:
Now we see that, if the curve is not y=0, there must be a point (x, y) on the curve where y≠0.
That would mean that (x, y) and (x,-y) are two different points on the curve and it is not the graph of a function, since it fails the vertical line test.
According to the vertical line test:
If every vertical line in the x- y plane intersects a given curve at most one point, then the curve is the graph of a function.
According to this statement: If the vertical line test holds good, then for each x-coordinate there is at most one y-coordinate giving a point on the curve. This y-coordinate would correspond to the value assigned to the x-coordinate.
Since there is only one y-coordinate, the assignment would be unique. This satisfies the definition ot a function which states that a function to be in existence, it is required that each element In the domain nas a unique element in the range.
Chapter 1 Prerequisites for Calculus Exercise 1.2 37E
Using the vertical line test we can see that the vertical line drawn on the curve intersects it more than once.
Therefore the given curve does not represent a function.
According to the vertical line test:
If every vertical line in the xy plane intersects a given curve at most one point, then the curve is the graph ot a function.
Chapter 1 Prerequisites for Calculus Exercise 1.2 38E
Chapter 1 Prerequisites for Calculus Exercise 1.2 39E
Chapter 1 Prerequisites for Calculus Exercise 1.2 40E
Chapter 1 Prerequisites for Calculus Exercise 1.2 41E
Chapter 1 Prerequisites for Calculus Exercise 1.2 42E
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Chapter 1 Prerequisites for Calculus Exercise 1.2 44E
Chapter 1 Prerequisites for Calculus Exercise 1.2 45E
Chapter 1 Prerequisites for Calculus Exercise 1.2 46E
Chapter 1 Prerequisites for Calculus Exercise 1.2 47E
Chapter 1 Prerequisites for Calculus Exercise 1.2 48E
Chapter 1 Prerequisites for Calculus Exercise 1.2 49E
The given function to sketch the graph is,
f(x) = -|3-x|+2
From our observation, the graph of the given function will be the graph of the absolute value function reflected across x-axis shifted by 3 units to the right and by 2 units upwards.
(a) Therefore the required graph will be:
[-9.4,9.4] by [-6.2,6.2]
(b) As the domain ot a function consists ot all the real values of x that give a real value of y.
Therefore the domain ot the given function is:
(-∞,2) for all real numbers.
(c) As we know the range of the function is given by all the real values attained by y when we replace x by all the different values in the domain.
Therefore, the range ot the function is:
(-∞,2]
Chapter 1 Prerequisites for Calculus Exercise 1.2 50E
The given function to sketch the graph is,
f(x) = 2|x+4|-3
From our observation, the graph of the given function will be the graph of the absolute value function reflected stretched vertically by a factor 2 and then shifted 4 units to the left and 3 units downwards.
(a) Therefore the required graph will be:
[-10,5] by [-5,10]
(b) As the domain ot a function consists ot all the real values of x that give a real value of y.
Therefore the domain ot the given function is:
(-∞,∞) for all real numbers.
(c) As we know the range of the function is given by all the real values attained by y when we replace x by all the different values in the domain.
Therefore, the range ot the function is:
[-3,∞)
Chapter 1 Prerequisites for Calculus Exercise 1.2 51E
Chapter 1 Prerequisites for Calculus Exercise 1.2 52E
Chapter 1 Prerequisites for Calculus Exercise 1.2 53E
Chapter 1 Prerequisites for Calculus Exercise 1.2 54E
(a) As required in the question we have to find the quadratic regression of the given data taking the assumption as x = 0 represent 1990, x = 1 represent 1991 and so on.
Therefore, 1997 will be x = 7 , 1998 will be x = 8 and so on.
These values when entered into a regression calculator (grapher) we get the quadratic regression equation.
Chapter 1 Prerequisites for Calculus Exercise 1.2 55E
As given in the question we have a circular paper ot 4in radius.
We cut out a piece ot sector ot arc length x,
then join the two edges ottne remaining portion to form a cone.
Chapter 1 Prerequisites for Calculus Exercise 1.2 56E
Chapter 1 Prerequisites for Calculus Exercise 1.2 57E
Chapter 1 Prerequisites for Calculus Exercise 1.2 58E
Chapter 1 Prerequisites for Calculus Exercise 1.2 59E
Chapter 1 Prerequisites for Calculus Exercise 1.2 60E
Chapter 1 Prerequisites for Calculus Exercise 1.2 61E
Chapter 1 Prerequisites for Calculus Exercise 1.2 62E
Chapter 1 Prerequisites for Calculus Exercise 1.2 63E
Chapter 1 Prerequisites for Calculus Exercise 1.2 64E
Chapter 1 Prerequisites for Calculus Exercise 1.2 65E
Chapter 1 Prerequisites for Calculus Exercise 1.2 66E
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Chapter 1 Prerequisites for Calculus Exercise 1.2 67E
(a) The completed graph in the given Window for the function being even, will be as shown below:
(b) The completed graph in the given Window for the function being odd, will be as shown below:
Chapter 1 Prerequisites for Calculus Exercise 1.2 68E
Chapter 1 Prerequisites for Calculus Exercise 1.2 69E
Chapter 1 Prerequisites for Calculus Exercise 1.2 70E
(a) The completed graph in the given Window for the function being even, will be as shown below:
Chapter 1 Prerequisites for Calculus Exercise 1.2 71E
(d) The domain of a sum, difference, or product of two functions is the intersection of their domains.
Whereas the domain of the quotient of two functions is the intersection of their domains with any zeros of the denominator removed.
Chapter 1 Prerequisites for Calculus Exercise 1.2 72E
Chapter 1 Prerequisites for Calculus Exercise 1.2 73E
Chapter 1 Prerequisites for Calculus Exercise 1.2 74E
Chapter 1 Prerequisites for Calculus Exercise 1.2 75E
Chapter 1 Prerequisites for Calculus Exercise 1.2 71E
