Question

Which graph represents the function?

Answer 1

The graph in the attached figure

Explanation:

we have

1)
`f(x)=(x+2)^2` -----> For the interval (-∞,-1)

Note The value of x=-1 is a open circle ( is not included)

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the point (-2,0)

2)
`f\left(x\right)=\left|x\right|+1` ----> For the interval [-1,1]

Note The value of x=-1 and x=1 are closed circle ( both values are included)

This is an absolute function open upward

The vertex is the point (0,1)

3)
`f(x)=-√(x)` -----> For the interval (1,∞)

Note The value of x=1 is a open circle ( is not included)

The value of f(x) is negative for all values of x

therefore

The graph in the attached figure