Answer:
x ≥ -5
Step-by-step explanation:
If we have a translation to left c units, we write " x + c " in the function, and
If we have a translation to right c units, we write " x - c" in the function
If we have vertical translation up b units, we "add b to the function", and
If we have vertical translation down b units, we "subtract b to the function"
The parent function is 
Since translation left 5 units and up 3 units, we can write:
The domain is affected by the square root sign and we know the number under the square root CANNOT be negative, so we can say:
x + 5 ≥ 0
x ≥ -5
This is the domain.
The first one is the same amount of points
x-coordinates for the maximum points in any function f(x) by f'(x) =0 would be x = π/2 and x= 3π/2.
<h3>How to obtain the maximum value of a function?</h3>
To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.
we want to find x-coordinates for the maximum points in any function f(x) by f'(x) =0
Given f(x)= 4cos(2x -π)
In general 
from x = 0 to x = 2π :
when k =0 then x = π/2
when k =1 then x= π
when k =2 then x= 3π/2
when k =3 then x=2π
Thus, X-coordinates of maximum points are x = π/2 and x= 3π/2
Learn more about maximum of a function here:
brainly.com/question/13333267
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For this there is no exact square root but the closest it get is about 75.33
Problem 1 (on the left)
It appears we have an exponential function curve through the points (0,4) and (1,7)
The general exponential function is of the form
y = a*b^x
The value of 'a' is the y intercept or initial value. So a = 4
Plug in (x,y) = (1,7) to help solve for b
y = a*b^x
y = 4*b^x
7 = 4*b^1
7 = 4b
b = 7/4 = 1.75
Therefore, the function is y = 4*(1.75)^x
- Plug in x = 0 and you should get y = 4.
- Plug in x = 1 and you should get y = 7
These two facts help confirm we have the correct exponential equation.
<h3>Answer: y = 4*(1.75)^x</h3>
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Problem 2 (on the right)
The steps will follow the same idea as the previous question.
The exponential curve goes through (-1, 120) and (0,40)
We have a = 40 this time due to the y intercept (0,40)
Plug in the coordinates of the other point to find b
y = a*b^x
y = 40*b^x
120 = 40*b^(-1)
120 = 40/b
120b = 40
b = 40/120
b = 1/3
<h3>Answer: y = 40*(1/3)^x</h3>
