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28.11.2020

What is the average rate of change of the function g(x) = 4x from x = 1 to x = 5?

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24.06.2023, solved by verified expert

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General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Function NotationInterval Notation - [a, b]Average Rate of Change:

What is the average rate of change of the function, №17886828, 28.11.2020 20:23

Step-by-step explanation:

Step 1: Define

g(x) = 4x

Interval [1, 5]

Step 2: Find Change

Substitute in function and points [Average Rate of Change]:

What is the average rate of change of the function, №17886828, 28.11.2020 20:23

[Fraction] Multiply:

What is the average rate of change of the function, №17886828, 28.11.2020 20:23

[Fraction] Subtract:

What is the average rate of change of the function, №17886828, 28.11.2020 20:23

[Fraction] Divide:

What is the average rate of change of the function, №17886828, 28.11.2020 20:23

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Mathematics

What is the average rate of change of the function g(x) = 4x from x = 1 to x = 5?

Step-by-step answer

P Answered by PhD

1

$\displaystyle 4$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Function NotationInterval Notation - [a, b]Average Rate of Change: $\displaystyle \displaystyle \frac{f(b) - f(a)}{b - a}$

Step-by-step explanation:

Step 1: Define

g(x) = 4x

Interval [1, 5]

Step 2: Find Change

Substitute in function and points [Average Rate of Change]: $\displaystyle \displaystyle \frac{4(5) - 4(1)}{5 - 1}$ [Fraction] Multiply: $\displaystyle \displaystyle \frac{20 - 4}{5 - 1}$ [Fraction] Subtract: $\displaystyle \displaystyle \frac{16}{4}$ [Fraction] Divide: $\displaystyle 4$

Mathematics

Which set represents the range of the function shown? (5 points) {(−1, 5), (2, 8), (5, 3), (13, −4)} a {−1, 2, 5, 13} b {−4, 3, 5, 8} c {(5, −1), (8, 2), (3, 5), (−4, 13)} d {−4, −1, 2, 3, 5, 5, 8, 13} Question 2 (5 points) (03.01 LC) Given that h(x) = 3x − 19, find the value of x that makes h(x) = 71. (5 points) a 30 b 43 c 52 d 194 Question 3 (5 points) (03.02 MC) Given the function g(x) = −3x + 4, compare and contrast g(−2) and g(4). Choose the statement that is true concerning these two values. (5 points) a The value of g(−2) is smaller than

Step-by-step answer

P Answered by PhD

1

1) b. {−4, 3, 5, 8}
2) a. 30
3) d. The value of g(−2) is larger than the value of g(4).
4) b. − 1 over 2
5) d. y = −2x − 1
6) a. line through the points 0 comma 6 and 12 comma 0
7) a. It is increasing during the time interval 4 < x < 7 hours.
8) from x15 to x 25 is 4 - -16 = -20 degree change
25-15 = 10000 feet
-20/10=-2 degrees every 1000 feet.
9) Suppose that the function f(x) is the parrent function and the graph of the function g(x)=f(x)-a can be obtained from the graph of the parrent function f(x) by shifting down a units.
Rewrite the expression for the function in the following way:
g(x)=32x-9=32x+8-8-9=32x+8-17=f(x)-17.
This shows that the shift down is made by 17 units.
10) b. The graph of y = f(x) will shift down 9 units.
11) b. y + 1 = 5(x + 2)
12) c. f(x) = 2x + 5
13) b. y = 9
14) d. vertical line through the point 5 comma 0

Mathematics

50 points for algebra answers 1. what are the zeros of the function? f(x)=x3−x2−6x a. −3 , 0, and 2 b. −3 , 0, and 1 c. −2 , 0, and 3 d. −1 , 0, and 3 2. the equation h(t)=−16t2+19t+110 gives the height of a rock, in feet, t seconds after it is thrown from a cliff. what is the initial velocity when the rock is thrown? 3. factor. x2−6x+8 x2−6x+8= ( )( ) 4. what are the zeros of the function f(x)=x2+2x−35 ? there are two. 5. let f(x)=x2−6x+13 . what is the vertex form of f(x)? what is the minimum value of f(x)? 6. let f(x)=4x and g(x)=4x+1−2 . which

Step-by-step answer

P Answered by Specialist

18

1. C
2. UNKNOWN
3. (x-4)(x-2)
4. 5, -7
5. vertex=(3,4)
minimum value=4
6. UNKNOWN
7. 5/3
8. D
9. C

Mathematics

50 points for algebra answers 1. what are the zeros of the function? f(x)=x3−x2−6x a. −3 , 0, and 2 b. −3 , 0, and 1 c. −2 , 0, and 3 d. −1 , 0, and 3 2. the equation h(t)=−16t2+19t+110 gives the height of a rock, in feet, t seconds after it is thrown from a cliff. what is the initial velocity when the rock is thrown? 3. factor. x2−6x+8 x2−6x+8= ( )( ) 4. what are the zeros of the function f(x)=x2+2x−35 ? there are two. 5. let f(x)=x2−6x+13 . what is the vertex form of f(x)? what is the minimum value of f(x)? 6. let f(x)=4x and g(x)=4x+1−2 . which

Step-by-step answer

P Answered by Specialist

18

1. C
2. UNKNOWN
3. (x-4)(x-2)
4. 5, -7
5. vertex=(3,4)
minimum value=4
6. UNKNOWN
7. 5/3
8. D
9. C

Mathematics

1. the table shows values of a function . what is the average rate of change of over the interval from x = 5 to x = 9? show your work. x: 4 5 6 7 8 9 10 f(x): -4 -2 8 10 11 14 18 2. given f(x)=4x^2 +6x and g(x)=2x^2+13x+1, find (f/g)(x) . show your work. 3.given f(x)= x^2-6x+8 and g(x)= x-2, solve f(x)=g(x) using a table of values. show your work.

Step-by-step answer

P Answered by PhD

54

1. **A(x)=(f(x)-f(a))/(x-a)
*A is the name of this average rate of change function
*x - a represents the change in the input of the function f
*f(x) - f(a) represents the change in the function f as the input changes from a to x
From table: f(5)=-2
f(9)=14
(f(5)-f(9))/(5-9)=(-2-14)/-4=4
The average rate of change of over the interval from x = 5 to x = 9 is 4.

2. f(x)=4x²+6x, g(x)=2x²+13x+1
(f/g)(x)=(4x²+6x)/(2x²+13x+1)
Using the table of values- x:4,5,6,7,8,9
f(x): 88/85,155/116,180/151,238/190,304/233,378/280

3. f(x)=x²-6x+8, g(x)=x-2
f(x)=g(x)⇒x²-6x+8=x-2⇒x²-6x-x+8+2=0, x²-7x+10=0
x₁,₂=(7⁺₋√(7²-4*10))/2=(7⁺₋3)/2
x₁=5, x₂=2
Using the table of values solution is x=5 because 2 doesn't exist in the table of values.

Mathematics

1. the table shows values of a function . what is the average rate of change of over the interval from x = 5 to x = 9? show your work. x: 4 5 6 7 8 9 10 f(x): -4 -2 8 10 11 14 18 2. given f(x)=4x^2 +6x and g(x)=2x^2+13x+1, find (f/g)(x) . show your work. 3.given f(x)= x^2-6x+8 and g(x)= x-2, solve f(x)=g(x) using a table of values. show your work.

Step-by-step answer

P Answered by PhD

54

1. **A(x)=(f(x)-f(a))/(x-a)
*A is the name of this average rate of change function
*x - a represents the change in the input of the function f
*f(x) - f(a) represents the change in the function f as the input changes from a to x
From table: f(5)=-2
f(9)=14
(f(5)-f(9))/(5-9)=(-2-14)/-4=4
The average rate of change of over the interval from x = 5 to x = 9 is 4.

2. f(x)=4x²+6x, g(x)=2x²+13x+1
(f/g)(x)=(4x²+6x)/(2x²+13x+1)
Using the table of values- x:4,5,6,7,8,9
f(x): 88/85,155/116,180/151,238/190,304/233,378/280

3. f(x)=x²-6x+8, g(x)=x-2
f(x)=g(x)⇒x²-6x+8=x-2⇒x²-6x-x+8+2=0, x²-7x+10=0
x₁,₂=(7⁺₋√(7²-4*10))/2=(7⁺₋3)/2
x₁=5, x₂=2
Using the table of values solution is x=5 because 2 doesn't exist in the table of values.

Biology

Between x = 2 and x = 3, which function has a larger average rate of change than f(x) = 2x has? A) g(x) = (2/3)−x B) k(x) = 5x−2 C) h(x) = 4x−1 D) j(x) = (1/2)−x+1

Step-by-step answer

P Answered by Specialist

6

The right answer is C.

Explanation:

I just did it on usatestprep.

Mathematics

Consider the table of values for function f. x: -1, 0, 1, 2, 3, 4, 5 f(x): 3.5, 4, 5, 7, 11, 19, 35 the function g is shown below: g(x)=4x+5 in which of the following intervals is the average rate of change greater for f than for g? a. [1,3] b. [3,5] c. [0,2] d. [-1,0]

Step-by-step answer

P Answered by PhD

12

B. [3,5]

Step-by-step explanation:

The rate of change of a function is the same as the slope between two given points from that same function,

Hence,

all we need to do is use the slope's equation, that is

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

And eval it in every couple of ordered pairs given from the table we obtain the following>

x2y2x1y1 m

04-13,5 0,5

1504 1

2715 2

31127 4

419311 8

535419 16

The rate of change from g(x) is 4 (its slope)

Hence, the interval when the rate of change of f(x) is greater than g(x) is from x=3 to x=5

Mathematics

Consider the table of values for function f. x: -1, 0, 1, 2, 3, 4, 5 f(x): 3.5, 4, 5, 7, 11, 19, 35 the function g is shown below: g(x)=4x+5 in which of the following intervals is the average rate of change greater for f than for g? a. [1,3] b. [3,5] c. [0,2] d. [-1,0]

Step-by-step answer

P Answered by PhD

12

B. [3,5]

Step-by-step explanation:

The rate of change of a function is the same as the slope between two given points from that same function,

Hence,

all we need to do is use the slope's equation, that is

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

And eval it in every couple of ordered pairs given from the table we obtain the following>

x2y2x1y1 m

04-13,5 0,5

1504 1

2715 2

31127 4

419311 8

535419 16

The rate of change from g(x) is 4 (its slope)

Hence, the interval when the rate of change of f(x) is greater than g(x) is from x=3 to x=5

Biology

Between x = 2 and x = 3, which function has a larger average rate of change than f(x) = 2x has? A) g(x) = (2/3)−x B) k(x) = 5x−2 C) h(x) = 4x−1 D) j(x) = (1/2)−x+1

Step-by-step answer

P Answered by Specialist

6

The right answer is C.

Explanation:

I just did it on usatestprep.

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