the values for the product of the functions f ( x ) = 2 x + 3 and h ( x ) = − 3 x − 12 , at x = − 2 , x = − 1 , x = 0 , x = 1 and x = 2 , graph component piece functions and their product.

Question

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Answer 1

Question

Chapter 1.2, Problem 22E

To determine

To calculate:the values for the product of the functions f(x)=2x+3 and h(x)=−3x−12 , at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Expert Solution & Answer

Answer to Problem 22E

The value of the functions and product of the functions for different values of x are,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

The graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 1

Explanation of Solution

Given information:

The functions, f(x)=2x+3 and h(x)=−3x−12 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, f(x)=2x+3 and g(x)=3x−5 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of f(x)⋅h(x) that is product of the functions,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36

Combine the like terms,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36=−6x2−33x−36

Therefore, the value of product of the function is −6x2−33x−36 .

Now, evaluate the value of the individual function f(x)=2x+3 , h(x)=−3x−12 and product of the function, f(x)⋅h(x)=−6x2−33x−36 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=6x2−x−15 .

f(−2)=2(−2)+3=−4+3=−1

Next,

h(−2)=−3(−2)−12=6−12=−6

Last,

f(−2)⋅h(−2)=−6(−2)2−33(−2)−36=−24+66−36=6

For x=−1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(−1)=2(−1)+3=−2+3=1

Next,

h(−1)=−3(−1)−12=3−12=−9

Last,

f(−1)⋅h(−1)=−6(−1)2−33(−1)−36=−6+33−36=−9

For x=0 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(0)=2(0)+3=3

Next,

h(0)=−3(0)−12=−12

Last,

f(0)⋅h(0)=−6(0)2−33(0)−36=−36

For x=1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(1)=2(1)+3=2+3=5

Next,

h(1)=−3(1)−12=−3−12=−15

Last,

f(1)⋅h(1)=−6(1)2−33(1)−36=−6−33−36=−75

For x=2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(2)=2(2)+3=4+3=7

Next,

h(2)=−3(2)−12=−6−12=−18

Last,

f(2)⋅h(2)=−6(2)2−33(2)−36=−24−66−36=−126

Thus, the above results are tabulated as,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

Plot the graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

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8. In the following check to see if the set S is a vector subspace of the corresponding Rn. If it is not, explain why not. If it is, then find a basis and the dimension. X1 (a) S = X2 {[2], n ≤ n } c X1 X2 CR² X1 (b) S X2 = X3 X4 x1 + x2 x3 = 0

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Answer 2

Question

Chapter 1.2, Problem 22E

To determine

To calculate:the values for the product of the functions f(x)=2x+3 and h(x)=−3x−12 , at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Expert Solution & Answer

Answer to Problem 22E

The value of the functions and product of the functions for different values of x are,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

The graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 1

Explanation of Solution

Given information:

The functions, f(x)=2x+3 and h(x)=−3x−12 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, f(x)=2x+3 and g(x)=3x−5 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of f(x)⋅h(x) that is product of the functions,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36

Combine the like terms,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36=−6x2−33x−36

Therefore, the value of product of the function is −6x2−33x−36 .

Now, evaluate the value of the individual function f(x)=2x+3 , h(x)=−3x−12 and product of the function, f(x)⋅h(x)=−6x2−33x−36 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=6x2−x−15 .

f(−2)=2(−2)+3=−4+3=−1

Next,

h(−2)=−3(−2)−12=6−12=−6

Last,

f(−2)⋅h(−2)=−6(−2)2−33(−2)−36=−24+66−36=6

For x=−1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(−1)=2(−1)+3=−2+3=1

Next,

h(−1)=−3(−1)−12=3−12=−9

Last,

f(−1)⋅h(−1)=−6(−1)2−33(−1)−36=−6+33−36=−9

For x=0 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(0)=2(0)+3=3

Next,

h(0)=−3(0)−12=−12

Last,

f(0)⋅h(0)=−6(0)2−33(0)−36=−36

For x=1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(1)=2(1)+3=2+3=5

Next,

h(1)=−3(1)−12=−3−12=−15

Last,

f(1)⋅h(1)=−6(1)2−33(1)−36=−6−33−36=−75

For x=2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(2)=2(2)+3=4+3=7

Next,

h(2)=−3(2)−12=−6−12=−18

Last,

f(2)⋅h(2)=−6(2)2−33(2)−36=−24−66−36=−126

Thus, the above results are tabulated as,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

Plot the graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 1.2, Problem 22E

To determine

To calculate:the values for the product of the functions f(x)=2x+3 and h(x)=−3x−12 , at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Expert Solution & Answer

Answer to Problem 22E

The value of the functions and product of the functions for different values of x are,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

The graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 1

Explanation of Solution

Given information:

The functions, f(x)=2x+3 and h(x)=−3x−12 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, f(x)=2x+3 and g(x)=3x−5 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of f(x)⋅h(x) that is product of the functions,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36

Combine the like terms,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36=−6x2−33x−36

Therefore, the value of product of the function is −6x2−33x−36 .

Now, evaluate the value of the individual function f(x)=2x+3 , h(x)=−3x−12 and product of the function, f(x)⋅h(x)=−6x2−33x−36 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=6x2−x−15 .

f(−2)=2(−2)+3=−4+3=−1

Next,

h(−2)=−3(−2)−12=6−12=−6

Last,

f(−2)⋅h(−2)=−6(−2)2−33(−2)−36=−24+66−36=6

For x=−1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(−1)=2(−1)+3=−2+3=1

Next,

h(−1)=−3(−1)−12=3−12=−9

Last,

f(−1)⋅h(−1)=−6(−1)2−33(−1)−36=−6+33−36=−9

For x=0 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(0)=2(0)+3=3

Next,

h(0)=−3(0)−12=−12

Last,

f(0)⋅h(0)=−6(0)2−33(0)−36=−36

For x=1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(1)=2(1)+3=2+3=5

Next,

h(1)=−3(1)−12=−3−12=−15

Last,

f(1)⋅h(1)=−6(1)2−33(1)−36=−6−33−36=−75

For x=2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(2)=2(2)+3=4+3=7

Next,

h(2)=−3(2)−12=−6−12=−18

Last,

f(2)⋅h(2)=−6(2)2−33(2)−36=−24−66−36=−126

Thus, the above results are tabulated as,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

Plot the graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 1.2, Problem 22E

To determine

To calculate:the values for the product of the functions f(x)=2x+3 and h(x)=−3x−12 , at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Expert Solution & Answer

Answer to Problem 22E

The value of the functions and product of the functions for different values of x are,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

The graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 1

Explanation of Solution

Given information:

The functions, f(x)=2x+3 and h(x)=−3x−12 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, f(x)=2x+3 and g(x)=3x−5 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of f(x)⋅h(x) that is product of the functions,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36

Combine the like terms,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36=−6x2−33x−36

Therefore, the value of product of the function is −6x2−33x−36 .

Now, evaluate the value of the individual function f(x)=2x+3 , h(x)=−3x−12 and product of the function, f(x)⋅h(x)=−6x2−33x−36 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=6x2−x−15 .

f(−2)=2(−2)+3=−4+3=−1

Next,

h(−2)=−3(−2)−12=6−12=−6

Last,

f(−2)⋅h(−2)=−6(−2)2−33(−2)−36=−24+66−36=6

For x=−1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(−1)=2(−1)+3=−2+3=1

Next,

h(−1)=−3(−1)−12=3−12=−9

Last,

f(−1)⋅h(−1)=−6(−1)2−33(−1)−36=−6+33−36=−9

For x=0 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(0)=2(0)+3=3

Next,

h(0)=−3(0)−12=−12

Last,

f(0)⋅h(0)=−6(0)2−33(0)−36=−36

For x=1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(1)=2(1)+3=2+3=5

Next,

h(1)=−3(1)−12=−3−12=−15

Last,

f(1)⋅h(1)=−6(1)2−33(1)−36=−6−33−36=−75

For x=2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(2)=2(2)+3=4+3=7

Next,

h(2)=−3(2)−12=−6−12=−18

Last,

f(2)⋅h(2)=−6(2)2−33(2)−36=−24−66−36=−126

Thus, the above results are tabulated as,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

Plot the graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 1.2, Problem 22E

To determine

To calculate:the values for the product of the functions f(x)=2x+3 and h(x)=−3x−12 , at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Expert Solution & Answer

Answer to Problem 22E

The value of the functions and product of the functions for different values of x are,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

The graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 1

Explanation of Solution

Given information:

The functions, f(x)=2x+3 and h(x)=−3x−12 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, f(x)=2x+3 and g(x)=3x−5 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of f(x)⋅h(x) that is product of the functions,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36

Combine the like terms,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36=−6x2−33x−36

Therefore, the value of product of the function is −6x2−33x−36 .

Now, evaluate the value of the individual function f(x)=2x+3 , h(x)=−3x−12 and product of the function, f(x)⋅h(x)=−6x2−33x−36 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=6x2−x−15 .

f(−2)=2(−2)+3=−4+3=−1

Next,

h(−2)=−3(−2)−12=6−12=−6

Last,

f(−2)⋅h(−2)=−6(−2)2−33(−2)−36=−24+66−36=6

For x=−1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(−1)=2(−1)+3=−2+3=1

Next,

h(−1)=−3(−1)−12=3−12=−9

Last,

f(−1)⋅h(−1)=−6(−1)2−33(−1)−36=−6+33−36=−9

For x=0 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(0)=2(0)+3=3

Next,

h(0)=−3(0)−12=−12

Last,

f(0)⋅h(0)=−6(0)2−33(0)−36=−36

For x=1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(1)=2(1)+3=2+3=5

Next,

h(1)=−3(1)−12=−3−12=−15

Last,

f(1)⋅h(1)=−6(1)2−33(1)−36=−6−33−36=−75

For x=2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(2)=2(2)+3=4+3=7

Next,

h(2)=−3(2)−12=−6−12=−18

Last,

f(2)⋅h(2)=−6(2)2−33(2)−36=−24−66−36=−126

Thus, the above results are tabulated as,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

Plot the graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

Answer 6

Chapter 1.2, Problem 22E

To determine

To calculate:the values for the product of the functions f(x)=2x+3 and h(x)=−3x−12 , at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Expert Solution & Answer

Answer to Problem 22E

The value of the functions and product of the functions for different values of x are,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

The graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 1

Explanation of Solution

Given information:

The functions, f(x)=2x+3 and h(x)=−3x−12 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, f(x)=2x+3 and g(x)=3x−5 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of f(x)⋅h(x) that is product of the functions,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36

Combine the like terms,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36=−6x2−33x−36

Therefore, the value of product of the function is −6x2−33x−36 .

Now, evaluate the value of the individual function f(x)=2x+3 , h(x)=−3x−12 and product of the function, f(x)⋅h(x)=−6x2−33x−36 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=6x2−x−15 .

f(−2)=2(−2)+3=−4+3=−1

Next,

h(−2)=−3(−2)−12=6−12=−6

Last,

f(−2)⋅h(−2)=−6(−2)2−33(−2)−36=−24+66−36=6

For x=−1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(−1)=2(−1)+3=−2+3=1

Next,

h(−1)=−3(−1)−12=3−12=−9

Last,

f(−1)⋅h(−1)=−6(−1)2−33(−1)−36=−6+33−36=−9

For x=0 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(0)=2(0)+3=3

Next,

h(0)=−3(0)−12=−12

Last,

f(0)⋅h(0)=−6(0)2−33(0)−36=−36

For x=1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(1)=2(1)+3=2+3=5

Next,

h(1)=−3(1)−12=−3−12=−15

Last,

f(1)⋅h(1)=−6(1)2−33(1)−36=−6−33−36=−75

For x=2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(2)=2(2)+3=4+3=7

Next,

h(2)=−3(2)−12=−6−12=−18

Last,

f(2)⋅h(2)=−6(2)2−33(2)−36=−24−66−36=−126

Thus, the above results are tabulated as,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

Plot the graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

Answer 7

Chapter 1.2, Problem 22E

To determine

To calculate:the values for the product of the functions f(x)=2x+3 and h(x)=−3x−12 , at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Answer 8

Expert Solution & Answer

Answer to Problem 22E

The value of the functions and product of the functions for different values of x are,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

The graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 is provided below,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 1

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given information:

The functions, f(x)=2x+3 and h(x)=−3x−12 .

Formula used:

The multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Calculation:

Consider the provided functions, f(x)=2x+3 and g(x)=3x−5 .

Recall the multiplication or product of the functions f and g is represented as f⋅g , mathematically it is denoted by,

(f⋅g)(x)=f(x)⋅g(x)

Evaluate the value of f(x)⋅h(x) that is product of the functions,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)

Multiply the first term of the first bracket with the terms in second bracket and do the same with the second term of the first bracket.

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36

Combine the like terms,

f(x)⋅h(x)=(2x+3)⋅(−3x−12)=2x(−3x−12)+3(−3x−12)=−6x2−24x−9x−36=−6x2−33x−36

Therefore, the value of product of the function is −6x2−33x−36 .

Now, evaluate the value of the individual function f(x)=2x+3 , h(x)=−3x−12 and product of the function, f(x)⋅h(x)=−6x2−33x−36 at the provided points x=−2,x=−1,x=0,x=1 and x=2 .

For x=−2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=6x2−x−15 .

f(−2)=2(−2)+3=−4+3=−1

Next,

h(−2)=−3(−2)−12=6−12=−6

Last,

f(−2)⋅h(−2)=−6(−2)2−33(−2)−36=−24+66−36=6

For x=−1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(−1)=2(−1)+3=−2+3=1

Next,

h(−1)=−3(−1)−12=3−12=−9

Last,

f(−1)⋅h(−1)=−6(−1)2−33(−1)−36=−6+33−36=−9

For x=0 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(0)=2(0)+3=3

Next,

h(0)=−3(0)−12=−12

Last,

f(0)⋅h(0)=−6(0)2−33(0)−36=−36

For x=1 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(1)=2(1)+3=2+3=5

Next,

h(1)=−3(1)−12=−3−12=−15

Last,

f(1)⋅h(1)=−6(1)2−33(1)−36=−6−33−36=−75

For x=2 , substitute the value of x in the functions, f(x)=2x+3 , h(x)=−3x−12 and f(x)⋅h(x)=−6x2−33x−36 .

f(2)=2(2)+3=4+3=7

Next,

h(2)=−3(2)−12=−6−12=−18

Last,

f(2)⋅h(2)=−6(2)2−33(2)−36=−24−66−36=−126

Thus, the above results are tabulated as,

xf(x)h(x)( f⋅h)(x)−2−1−66−11−9−903−12−3615−15−7527−18−126

Plot the graph of the functions f(x)=2x+3 , h(x)=−3x−12 and (f⋅h)(x)=−6x2−33x−36 on the same coordinate axes and visualize the each of them.

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 1.2, Problem 22E , additional homework tip 2

Thus, the results obtained graphically and mathematically are same.

Answer 12

Ch. 1.2 - Identify the variables and parameters in the...Ch. 1.2 - Prob. 2E Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Graph the given points and say which point does...Ch. 1.2 - Graph the given points and say which point does...Ch. 1.2 - Graph the given points and say which point does...Ch. 1.2 - Graph the given points and say which point does...

the values for the product of the functions f ( x ) = 2 x + 3 and h ( x ) = − 3 x − 12 , at x = − 2 , x = − 1 , x = 0 , x = 1 and x = 2 , graph component piece functions and their product.

To calculate:the values for the product of the functions f(x)=2x+3 and h(x)=−3x−12 , at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their product.

Answer to Problem 22E

Explanation of Solution

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