Question

Which graph represents the function?

Answer 1

Answer:

The graph in the attached figure

Step-by-step 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) $f(x)=-\sqrt{x}$ -----> 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