What is the range for the following function? y=1/(x+2)+3
a){y: y∈ℝ, y≠-2}
b){y: y∈ℝ, y≠2}
c){y: y∈ℝ, y≠3}
d){y: y∈ℝ}

Step-by-step explanation:

The range is the spread of the y-values (minimum to maximum distance travelled).

The graph of your function is a hyperbola shifted two units left and three units up from the origin.

There is a vertical asymptote at x = -2, so y does not exist when x = -2.  However,

Since the limit from either side is the same,

The graph below shows the asymptotes of your function.

Thus. y can take any value  except 3.

In set builder notation, the range is  

solve systems of equations by graphing. a system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. the solution of such a system is the ordered pair that is a solution to both equations. to solve a system of linear equations graphically we graph both equations in the same coordinate system