The graph of the function
![f(x) =-x^2-4x + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D-x%5E2-4x%20%2B%202)
is parabola with branches going down in the negative direction of y-axis.
The vertex of parabola has coordinates:
![x_v=\dfrac{-(-4)}{2\cdot(-1)}=-2, \\ y_v=-(-2)^2-4\cdot (-2)+2=-4+8+2=6](https://tex.z-dn.net/?f=x_v%3D%5Cdfrac%7B-%28-4%29%7D%7B2%5Ccdot%28-1%29%7D%3D-2%2C%20%5C%5C%20y_v%3D-%28-2%29%5E2-4%5Ccdot%20%28-2%29%2B2%3D-4%2B8%2B2%3D6)
Then you can conclude that all x are possible, that means that the dimain is
![x\in (-\infty,\infty)](https://tex.z-dn.net/?f=x%5Cin%20%28-%5Cinfty%2C%5Cinfty%29)
and the maximum value of y is at the vertex, then the range is
![(-\infty,6]](https://tex.z-dn.net/?f=%28-%5Cinfty%2C6%5D)
.The function is increasing for x<-2 and decreasing for x>-2 (since vertex is the maximum point).
When x=0, y=2.
Hence,
<span>The domain is {x|x ≤ –2} - false.
</span>
<span>The range is {y|y ≤ 6} - true.
</span>
<span>The function is increasing over the interval (–∞ , –2) - true.
</span>
<span>The function is decreasing over the interval (−4, ∞) - false.
</span>
<span>The function has a positive y-intercept - true.</span>