Calculus: Graphical, Numerical, Algebraic, 3rd Edition Answers Ch 1 Prerequisites for Calculus Ex 1.6
Calculus: Graphical, Numerical, Algebraic Answers
Chapter 1 Prerequisites for Calculus Exercise 1.6 1E
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The given point is P(0,—3)
As we know that for a vertical line we have m=∞ (undefined)
In case of a vertical line we can see that the x-coordinate does not change but remains constant.
Therefore, the required equation is, x = 0
Chapter 1 Prerequisites for Calculus Exercise 1.6 4E
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Chapter 1 Prerequisites for Calculus Exercise 1.6 5E
We know that if a function is even then f(-x) = f(x)
And if a function is odd then f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.6 5QR
Chapter 1 Prerequisites for Calculus Exercise 1.6 5RE
Chapter 1 Prerequisites for Calculus Exercise 1.6 6E
We know that if a function is even then f(-x) = f(x)
And if a function is odd then f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.6 6QR
Chapter 1 Prerequisites for Calculus Exercise 1.6 6RE
Chapter 1 Prerequisites for Calculus Exercise 1.6 7E
We know that if a function is even then f(-x) = f(x)
And if a function is odd then f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.6 7QR
Chapter 1 Prerequisites for Calculus Exercise 1.6 7RE
Given slope is m = —3 and the y-intercept b = 3
As we know that the slope-intercept torm ot equation is given by
y = mx + b
Where,
m is the slope of the line,
b is the given y intercept of the line,
Therefore, trom the given values the equation will be
y = -3x+(3)
= -3x+3
Chapter 1 Prerequisites for Calculus Exercise 1.6 8E
We know that if a function is even then f(-x) = f(x)
And if a function is odd then f(-x) = -f(x)
Chapter 1 Prerequisites for Calculus Exercise 1.6 8QR
Chapter 1 Prerequisites for Calculus Exercise 1.6 8RE
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Symmetry about y-axis:
To check the symmetry about y- axis, we change x to –x and see if the equation remains unchanged. In this case changing x to –x changes the equation. Therefore the curve is not symmetric to y-axis.
Symmetry about origin:
To check the symmetry about origin, we simultaneously change x to –x and y to –y and see if the equation remains unchanged. In this case the equation does not remain same. Therefore the curve is not symmetric to origin.
Hence the curve is neither symmetric to y-axis nor to the origin.
Chapter 1 Prerequisites for Calculus Exercise 1.6 18E
Chapter 1 Prerequisites for Calculus Exercise 1.6 18RE
From the above graphical representation of the given function we can say that the given function is symmetric about the y-axis.
(OR)
To check the symmetry about y-axis, we replace x with –x and see if the equation remains unchanged. In this case the equation remains unchanged. Therefore the curve is symmetric about y-axis
Chapter 1 Prerequisites for Calculus Exercise 1.6 19E
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(d) The given equation might not be a good model for Susan’s guppy population because it suggests that the number of guppies will continue to double in definitely and become arbitrarily large, which is impossible due to the finite size of the tank and the oxygen supply in the water.
Chapter 1 Prerequisites for Calculus Exercise 1.6 66RE
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