Answer:
f(x + 1) = 3x² + 5x + 7
Step-by-step explanation:
To find f(x + 1), substitute x = x + 1 into f(x), that is
f(x + 1) = 3(x + 1)² - (x + 1) + 5 ← expand (x + 1)² using FOIL
= 3(x² + 2x + 1) - x - 1 + 5 ← distribute parenthesis by 3
= 3x² + 6x + 3 - x - 1 + 5 ← collect like terms
= 3x² + 5x + 7
Answer:
Step-by-step explanation:
Given a function
, we called the rate of change to the number that represents the increase or decrease that the function experiences when increasing the independent variable from one value "
" to another "
".
The rate of change of
between
and
can be calculated as follows:
![Rate\hspace{3}of\hspace{3}change=f(x_2)-f(x_1)](https://tex.z-dn.net/?f=Rate%5Chspace%7B3%7Dof%5Chspace%7B3%7Dchange%3Df%28x_2%29-f%28x_1%29)
For:
![f(x)=x^2-2x+4](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2-2x%2B4)
Let's find
and
, where:
![[x_1,x_2]=[-4,3]](https://tex.z-dn.net/?f=%5Bx_1%2Cx_2%5D%3D%5B-4%2C3%5D)
![f(x_1)=f(-4)=(-4)^2-2(4)+4=16-8+4=12\\f(x_2)=f(3)=(3)^2-2(3)+4=9-6+4=7](https://tex.z-dn.net/?f=f%28x_1%29%3Df%28-4%29%3D%28-4%29%5E2-2%284%29%2B4%3D16-8%2B4%3D12%5C%5Cf%28x_2%29%3Df%283%29%3D%283%29%5E2-2%283%29%2B4%3D9-6%2B4%3D7)
So:
![Rate\hspace{3}of\hspace{3}change =7-12=-5\hspace{3}Negative](https://tex.z-dn.net/?f=Rate%5Chspace%7B3%7Dof%5Chspace%7B3%7Dchange%20%3D7-12%3D-5%5Chspace%7B3%7DNegative)
And for:
![f(x)-3x+2](https://tex.z-dn.net/?f=f%28x%29-3x%2B2)
Let's find
and
, where:
![[x_1,x_2]=[-4,3]](https://tex.z-dn.net/?f=%5Bx_1%2Cx_2%5D%3D%5B-4%2C3%5D)
![f(x_1)=f(-4)=-3(-4)+2=12+2=14\\f(x_2)=f(3)=-3(3)+2=-9+2=-7](https://tex.z-dn.net/?f=f%28x_1%29%3Df%28-4%29%3D-3%28-4%29%2B2%3D12%2B2%3D14%5C%5Cf%28x_2%29%3Df%283%29%3D-3%283%29%2B2%3D-9%2B2%3D-7)
So:
![Rate\hspace{3}of\hspace{3}change =-7-14=-21\hspace{3}Negative](https://tex.z-dn.net/?f=Rate%5Chspace%7B3%7Dof%5Chspace%7B3%7Dchange%20%3D-7-14%3D-21%5Chspace%7B3%7DNegative)
<em>Translation:</em>
Dada una función
, llamábamos tasa de variación al número que representa el aumento o disminución que experimenta la función al aumentar la variable independiente de un valor "
" a otro "
".
La tasa de variación de
entre
y
, puede ser calculada de la siguiente forma:
![Tasa\hspace{3}de\hspace{3}variacion=f(x_2)-f(x_1)](https://tex.z-dn.net/?f=Tasa%5Chspace%7B3%7Dde%5Chspace%7B3%7Dvariacion%3Df%28x_2%29-f%28x_1%29)
Para:
![f(x)=x^2-2x+4](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2-2x%2B4)
Encontremos
y
, donde:
![[x_1,x_2]=[-4,3]](https://tex.z-dn.net/?f=%5Bx_1%2Cx_2%5D%3D%5B-4%2C3%5D)
![f(x_1)=f(-4)=-3(-4)+2=12+2=14\\f(x_2)=f(3)=-3(3)+2=-9+2=-7](https://tex.z-dn.net/?f=f%28x_1%29%3Df%28-4%29%3D-3%28-4%29%2B2%3D12%2B2%3D14%5C%5Cf%28x_2%29%3Df%283%29%3D-3%283%29%2B2%3D-9%2B2%3D-7)
Entonces:
![Tasa\hspace{3}de\hspace{3}variacion =7-12=-5\hspace{3}Negativa](https://tex.z-dn.net/?f=Tasa%5Chspace%7B3%7Dde%5Chspace%7B3%7Dvariacion%20%3D7-12%3D-5%5Chspace%7B3%7DNegativa)
Y para:
![f(x)-3x+2](https://tex.z-dn.net/?f=f%28x%29-3x%2B2)
Encontremos
y
, donde:
![[x_1,x_2]=[-4,3]](https://tex.z-dn.net/?f=%5Bx_1%2Cx_2%5D%3D%5B-4%2C3%5D)
![f(x_1)=f(-4)=-3(-4)+2=12+2=14\\f(x_2)=f(3)=-3(3)+2=-9+2=-7](https://tex.z-dn.net/?f=f%28x_1%29%3Df%28-4%29%3D-3%28-4%29%2B2%3D12%2B2%3D14%5C%5Cf%28x_2%29%3Df%283%29%3D-3%283%29%2B2%3D-9%2B2%3D-7)
Entonces:
![Tasa\hspace{3}de\hspace{3}variacion=-7-14=-21\hspace{3}Negativa](https://tex.z-dn.net/?f=Tasa%5Chspace%7B3%7Dde%5Chspace%7B3%7Dvariacion%3D-7-14%3D-21%5Chspace%7B3%7DNegativa)
Answer: (644 - 200) / 12 = x
Step-by-step explanation:
To find the number of albums Floyd sold, first, subtract $200 dollars (the base rate) from his total profit of $644. This gives you a result of $444. Then, divide $444 by $12 (the amount made per album sold) to get a result of 37 albums sold. The equation for this is (644 - 200) / 12 = x.
Answer:
sjajaajjsjsnznnznznznznnzn,n,nznznznznznnznnznzbzbdbdbxbxbxvxcxbbcbvcbbx
Step-by-step explanation:
bb a anan
。☆✼★ ━━━━━━━━━━━━━━ ☾
Yes, it is.
Positive numbers are greater than negative numbers.
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
。☆✼★ ━━━━━━━━━━━━━━ ☾