The parent function for quadratic equations is as followed:
![y=a(bx-h)+k](https://tex.z-dn.net/?f=y%3Da%28bx-h%29%2Bk)
where a and b represent vertical and horizontal stretches, respectively, h is the horizontal shift, and k is the vertical shift.
So going from
![(3x)^2](https://tex.z-dn.net/?f=%283x%29%5E2)
to
![(3x+1)^2+6](https://tex.z-dn.net/?f=%283x%2B1%29%5E2%2B6)
,
We are shifting 1 to the left and 6 up.
The horizontal shift is in the negative direction because in the equation, h=-1 because:
The answer is A.
Answer:
![\left \{ {{f(x)=2;\text{ For }0\leq x1}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bf%28x%29%3D2%3B%5Ctext%7B%20For%20%7D0%5Cleq%20x%3C1%7D%5C%5C%5C%5C%5C%5C%5C%5C%20%5Catop%20%7Bf%28x%29%3D-%5Csqrt%7Bx-1%7D%2B1%3B%5Ctext%7B%20For%20%7Dx%3E1%7D%7D%20%5Cright.)
Step-by-step explanation:
We have been given graph of a piece-wise function. We are asked to write the equation for the given piece-wise function.
We can see that for x values greater than or equal to 0 and less than 1, the function is a line.
We can see that our given line is a horizontal line, so it will be in form
intersecting y-axis at
.
The given crosses y-axis at (0,2), therefore, its equation would be
.
We can see that for x values greater than 1, the graph is a reflected and shifted square root function.
The square root function is reflected across x-axis and has a vertex at (1,1), therefore, our function for second part would be
.
The function is not defined at
and it can a jump continuity.
Therefore, our required piece-wise function would be:
![\left \{ {{f(x)=2;\text{ For }0\leq x1}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bf%28x%29%3D2%3B%5Ctext%7B%20For%20%7D0%5Cleq%20x%3C1%7D%5C%5C%5C%5C%5C%5C%5C%5C%20%5Catop%20%7Bf%28x%29%3D-%5Csqrt%7Bx-1%7D%2B1%3B%5Ctext%7B%20For%20%7Dx%3E1%7D%7D%20%5Cright.)
Divide 2999 by 55 they YOU can round it to the nearest cent
5n = 25
divide both sides by 5
n = 5
Answer:
300-150
Step-by-step explanation:
300 deposited into bank account (+)
150 taken out of bank account (-)