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____ [38]
3 years ago
6

Which statement best describes the function below?

Mathematics
1 answer:
marta [7]3 years ago
6 0
<h2>Answer:</h2>

A. It is a many-to-one function.

<h2>Step-by-step explanation:</h2>

Hello! It will be a pleasure to help to figure out what's the correct answer to this problem. First of all, we have the following function:

f(x) = 2x^3 + 2x^2-x

When plotting this function, we get the red graph of the function shown below. So let's solve this as follows:

<h3>A. It is a many-to-one function.</h3>

True

A function is said to be many-to-one there are values of the dependent variable (y-values) that corresponds to more than one value of the independent variable (x-values). To test this, we need to use the Horizontal Line Test. So let's take the horizontal line y=0.5, and you can see from the first figure below that y=0.5 is mapped onto x=-1.241 \ x=-0.344 \ and \ x=0.585. so this is a many-to-one function.

<h3>B. It is a one-to-one function.</h3><h3>False</h3>

Since this is a many-to-one function, it can't be a one-to-one function.

<h3>C. It is not a function.</h3>

False

Indeed, this is a function

<h3>D. It fails the vertical line test.​</h3>

False

It passes the vertical line test because any vertical line can intersect the graph of the function at most once. An example of this is shown in the second figure below.

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Find the absolute maximum and minimum values of f(x,y)=xy−4x in the region bounded by the x-axis and the parabola y=16−x2.
skad [1K]

Answer:

The absolute maximum and minimum is 20\; \text{and} -20.

Step-by-step explanation:

We first check the critical points on the interior of the domain using the

first derivative test.

f_x=y-4=0

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The only solution to this system of equations is the point (0, 4), which lies in the domain.

f_{xx}=0, \;f_{yy}=0\; \text{and}\; f_{xy}=-1

\Rightarrow f_{xx}f_{yy}-f_{xy}=o-1=-1

\therefore (0,4) is a saddle point.

Boundary points -  (4,0),  (-4,0), (0,16)

Along boundary  y=16-x^2

   f=x(16-x^2)-4x

=16x-x^3-4x

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\Rightarrow 3x^2=12

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Values of f(x) at these points.

\begin{array}{}(4,0)=-16\\(-4,0)=16\\(0,16)=0\\(2,14)=20\\(-2,14)=-20\end{array}

Therefore, the absolute maximum and minimum is 20\; \text{and} -20.

6 0
3 years ago
What is pythagoras theorem​
Alborosie

Answer:

hypotenuse²=base²x height²

Step-by-step explanation:

It is used to find the third side of a triangle.

Hope it helps :)

6 0
3 years ago
A library is open til' 5:00 P.M. On Wednesdays, the library closes 2 hours early. How many hours for a month is the library open
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So
if you assume that the month has 30 days and that the library opens at midnight, then
24 hours in a day
5 pm=12+5=17 hours
on wednessday=17-2=15 hours
wednessday=1/7 of week
so we find 1/7 of 30 which is 30/7=4 and 2/7
then subtract that from 30
30-4 and 2/7=25 and 5/7

ok so then we have
25 and 5/7 days is 17 hours and
4 and 2/7 days is 15 hours
so just multipy them and add

25 and 5/7 times 17=437.143 hours
4 and 2/7 days times 15 =64.2857
add

437.143+64.2856=501.429
so aprox 501.429

the real equation is  [(\frac{1}{7})(n)(15)]+[ (\frac{6}{7}) (n)(17)]=hours where n represents the number of days in the month

apros 501.429
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<span>variance of </span>950 students
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