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}. the
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.
2 answers:
we have that
using a graph tool
see the attached figure
statements
case a) The domain is {x|x ≤ –2}-------> Is False
the domain is all real numbers---------> the interval (-∞,∞)
case b) The range is {y|y ≤ 6}.------> Is True
The range is the interval (-∞,6]
case c) The function is increasing over the interval (–∞ , –2).-----> Is True
See the attached figure
case d)The function is decreasing over the interval (−4, ∞).-----> Is False
In the interval (-4,-2) the function is increasing and in the interval (-2,∞) the function is decreasing (See the attached figure)
case e)The function has a positive y-intercept.------> Is True
The value of y-intercept is
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Usually one will differentiate the function to find the minimum/maximum point, but in this case differentiating yields:
which contains multiple solution if one tries to solve for x when the differentiated form is 0.
I would, though, venture a guess that the minimum value would be (approaching) 5, since the function would be undefined in the vicinity.
If, however, the function is
Then differentiating and equating to 0 yields:
which gives:
or 
We reject x=5 as it is when it ix the maximum and thus,
, for 
which contains multiple solution if one tries to solve for x when the differentiated form is 0.
I would, though, venture a guess that the minimum value would be (approaching) 5, since the function would be undefined in the vicinity.
If, however, the function is
Then differentiating and equating to 0 yields:
which gives:
We reject x=5 as it is when it ix the maximum and thus,