a. Answer The domain is ( − ∞ , ∞ ) . Explanation Given information: Let f ( x ) = 1 − 3 cos ( 2 x ) . Calculation: The graph of the function , using graphing utility is shown below. As the graph shows, as does any graph of a multiple of cos(x), the x-values (domain) decrease infinitely and increase infinitely. Around the infinities are parentheses, because the x-values never truly reach a set value. Therefore, the domain of function is ( − ∞ , ∞ ) . b. To determine To find : the range of f. Answer The range is ( − 2 , 4 ) . Explanation Given information: f ( x ) = 1 − 3 cos ( 2 x ) . Calculation: As the graph shows, the minimum y-value is -2 and the maximum y-value is 4. Around those numbers are brackets because the graph does reach those values, rather than approach them. Therefore, the range of function is ( − 2 , 4 ) c. To determine To find: the period of f. Answer The period of f is π . Explanation Given information: f ( x ) = 1 − 3 cos ( 2 x ) Calculation: The distance from the beginning of one period (0, -2) to the end of that period, ( π , − 2 ) , is π . Therefore, the period of f is π . d. To determine To find: is f an even function, odd function, or neither. Answer Even. Explanation Given information : f ( x ) = 1 − 3 cos ( 2 x ) . Calculation: A function is even if there is symmetry along the y-axis, as is the case with this graph. Therefore, f is an even function. e. To determine To find: all the zeros of f in π 2 ≤ x ≤ π . Answer x ≈ 2.526. Explanation Given information: f ( x ) = 1 − 3 cos ( 2 x ) . Calculation: π 2 ≈ 1.5707 and π ≈ 3.1415. The only time when the curve crosses the x −axis in between those numbers is found at 2,526. This can be found using the zeros function on graphing calculator.

Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 1, Problem 70RE

To determine

To find: the domain of f.

Expert Solution

Answer to Problem 70RE

The domain is (−∞,∞) .

Explanation of Solution

Given information: Let f(x)=1−3cos(2x) .

Calculation:

The graph of the function , using graphing utility is shown below.

Calculus: Graphical, Numerical, Algebraic, Chapter 1, Problem 70RE

As the graph shows, as does any graph of a multiple of cos(x), the x-values (domain) decrease infinitely and increase infinitely. Around the infinities are parentheses, because the x-values never truly reach a set value. Therefore, the domain of function is (−∞,∞) .

To determine

To find: the range of f.

Expert Solution

Answer to Problem 70RE

The range is (−2,4) .

Explanation of Solution

Given information: f(x)=1−3cos(2x) .

Calculation:

As the graph shows, the minimum y-value is -2 and the maximum y-value is 4. Around those numbers are brackets because the graph does reach those values, rather than approach them.

Therefore, the range of function is (−2,4)

To determine

To find: the period of f.

Expert Solution

Answer to Problem 70RE

The period of f is π .

Explanation of Solution

Given information: f(x)=1−3cos(2x)

Calculation:

The distance from the beginning of one period (0, -2) to the end of that period, (π,−2), is π.

Therefore, the period of f is π .

To determine

To find: is f an even function, odd function, or neither.

Expert Solution

Answer to Problem 70RE

Even.

Explanation of Solution

Given information: f(x)=1−3cos(2x) .

Calculation:

A function is even if there is symmetry along the y-axis, as is the case with this graph.

Therefore, f is an even function.

To determine

To find: all the zeros of f in π2≤x≤π .

Expert Solution

Answer to Problem 70RE

x≈2.526.

Explanation of Solution

Given information: f(x)=1−3cos(2x) .

Calculation:

π2≈1.5707 and π≈3.1415. The only time when the curve crosses the x −axis in between those numbers is found at 2,526. This can be found using the zeros function on graphing calculator.

Chapter 1, Problem 69RE

Chapter 2.1, Problem 1QR

Chapter 1 Solutions

Calculus: Graphical, Numerical, Algebraic

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

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