Hey guys I need your help on this!!
1 answer:
Answer:
Domain: (-∞, ∞) or All Real Numbers
Range: (0, ∞)
Asymptote: y = 0
As x ⇒ -∞, f(x) ⇒ 0
As x ⇒ ∞, f(x) ⇒ ∞
Step-by-step explanation:
The domain is talking about the x values, so where is x defined on this graph? That would be from -∞ to ∞, since the graph goes infinitely in both directions.
The range is from 0 to ∞. This where all values of y are defined.
An asymptote is where the graph cannot cross a certain point/invisible line. A y = 0, this is the case because it is infinitely approaching zero, without actually crossing. At first, I thought that x = 2 would also be an asymptote, but it is not, since it is at more of an angle, and if you graphed it further, you could see that it passes through 2.
The last two questions are somewhat easy. It is basically combining the domain and range. However, I like to label the graph the picture attached to help even more.
As x ⇒ -∞, f(x) ⇒ 0
As x ⇒ ∞, f(x) ⇒ ∞
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Answer:
C) The partial derivatives were not evaluated a the point.
D) The answer is not a linear function.
The correct equation for the tangent plane is or
Step-by-step explanation:
The equation of the tangent plane to a surface given by the function in a given point
can be obtained using:
(1)
where and
are the partial derivatives of
with respect to
and
respectively and evaluated at the point
.
Therefore we need to find two missing inputs in our problem in order to use equation (1). The coordinate and the partial derivatives
and
. For
just evaluating in the given function we obtain
and the partial derivatives are:
Now, substituting in (1)
Notice that until this point, we obtain the same equation as the student, however, we have not evaluated the partial derivatives and therefore this is not the equation of the plane and this is not a linear function because it contains the terms ( and
)
For finding the right equation of the tangent plane, let's substitute the values of the partial derivatives evaluated at the given point:
or