Answer:
To create function h, function f was translated 2 units right
, translated 4 units up and reflected across the x axis
Step-by-step explanation:
Given
![f(x) = x^3](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E3)
![h(x) =-(x + 2)^3 - 4](https://tex.z-dn.net/?f=h%28x%29%20%3D-%28x%20%2B%202%29%5E3%20-%204)
Required
Complete chart
First: f(x) was translated right by 2 units
The rule of right translation is ![(x,y) \to (x + 2,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%20%2B%202%2Cy%29)
So, we have:
![f'(x) = f(x + 2)](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20f%28x%20%2B%202%29)
![f'(x) = (x + 2)^3](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%28x%20%2B%202%29%5E3)
Next: f'(x) was translated up by 4 units
The rule of down translation is ![(x,y) \to (x,y+4)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%2Cy%2B4%29)
So, we have:
![f"(x) = f'(x) +4](https://tex.z-dn.net/?f=f%22%28x%29%20%3D%20f%27%28x%29%20%2B4)
![f"(x) = (x + 2)^3 +4](https://tex.z-dn.net/?f=f%22%28x%29%20%3D%20%28x%20%2B%202%29%5E3%20%2B4)
Lastly, f"(x) was reflected across the x-axis;
The rule of this reflection is: ![(x,y) \to (x,-y)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%2C-y%29)
So, we have:
![h(x) = -f"(x)](https://tex.z-dn.net/?f=h%28x%29%20%3D%20-f%22%28x%29)
![h(x) = -[(x+2)^3 + 4]](https://tex.z-dn.net/?f=h%28x%29%20%3D%20-%5B%28x%2B2%29%5E3%20%2B%204%5D)
Remove bracket
![h(x) = -(x+2)^3 - 4](https://tex.z-dn.net/?f=h%28x%29%20%3D%20-%28x%2B2%29%5E3%20-%204)
Answer:
180 yards.
Step-by-step explanation:
80% of 225 = 180.
(1,4) you go right 1 time, and than go up 4.
Answer:
The student is incorrect because I I or absolute value would make the -9 to positive 9.
Step-by-step explanation:
-9<4
on a numberline
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
but the absolute value of -9 (or) |–9|
is actually positive 9
9>4
on a number line
4 5 6 7 8 9