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musickatia [10]
3 years ago
5

Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Check all that apply. The domain is {x|x ≤ –2}. T

he range is {y|y ≤ 6}. The function is increasing over the interval (–∞ , –2). The function is decreasing over the interval (−4, ∞). The function has a positive y-intercept.
Mathematics
2 answers:
Leto [7]3 years ago
8 0
The graph of the function f(x) =-x^2-4x + 2 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

Then you can conclude that all x are possible, that means that the dimain is x\in (-\infty,\infty) and the maximum value of y is at the vertex, then the range is (-\infty,6].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>









Alex_Xolod [135]3 years ago
5 0

Answer:

The range is {y|y ≤ 6}

The function is increasing over the interval (–∞ , –2)

The function has a positive y-intercept

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