Unlocking the mystery of 1/(x+2)+2, the graph and analysis of function!

Deep Dive into the Graph of 1/(x+2) + 2

Identify the Denominator: In the function 1/(x+2) + 2, the denominator is x+2.
Set the Denominator Equal to Zero: To find where the function is undefined, set the denominator x+2 equal to zero.
Solve for x: Solving the equation x+2 = 0 gives x = -2.
Vertical Asymptote: Since the function becomes undefined at x = -2, this is where the vertical asymptote occurs.

Horizontal Asymptote: The graph has a horizontal asymptote at y = 2. As x moves towards positive or negative infinity, the graph approaches this line but never actually reaches it.
Quadrants: The graph is located in the 1st and 4th quadrants. This is because the function is shifted two units up.
End Behavior: As x approaches -2 from the left, the function value (y) dives towards negative infinity. As x approaches -2 from the right, the function value (y) soars towards positive infinity.
Curve Shape: The graph is hyperbolic, meaning it has a curve that gets closer and closer to the asymptotes but never actually touches them.
Shift: Compared to the graph of 1/x, this graph is shifted two units to the left and two units up, due to the “+2” in the denominator and the “+2” added to the function.