Please I need help with those question with the explanation

Please I need help with those question with the explanation

Find the domain of the function f(x) = Squareroot x + 2/x a. (-infinity, -2] b. [-2, infinity) c. [-2, 0) (0, infinity) d. [-infinity, 0) (0, infinity) e. [-2, 0) If you shift the graph of y = f(x) four units down and two to the left, you get the graph a. y = f(x+2)+4 b. y = f(x-2)+4 c. y=f(x-4)+2 d. y = f(x+4)-2 e. y = f(x+2)-4 Choose the piecewise function for the given graph a. {3, for, x>1 -1, for, x

Solution

1. domain of the function f(x) = sqrt(x+2)/2

Domain is related to the values x can take

Here we have a square root term

And we cant find out the square root of a negative term

Therefore x+2>=0

x>=-2

And its a rational term too and in a rational term the bottom cant be 0

Therefore the domain is

[-2,0) U (0,infinity)

Hence the correct option is c

2.y=f(x)

The function is shifted 4 units down

so we get y=f(x)-4

and It is shifted to 2 units to the left too

y=f(x+2)-4

The correct option is E