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pogonyaev
3 years ago
8

Describe the end behavior of polynomial graphs with odd and even degrees. Talk about positive and negative leading coefficients.

Mathematics
2 answers:
Oxana [17]3 years ago
8 0
<h2>Answer with explanation:</h2>

The general polynomial function is given by:

P(x)=a_nx^n+a_{n-1}x^{n-1}+.....+a_1x+a_0

where a_n\neq 0 and it is the leading coefficient.

Also, if n is even then it is a even degree polynomial.

and if n is odd then it is a odd degree polynomial.

The end behavior of a polynomial is the behavior when x tends to infinity from both the sides.

i.e. when x → -∞ and when x → ∞

Now,

<u>If n is even:</u>

1)

a_n\ \text{is positive}

then if x → -∞  then P(x) → ∞

and if x → ∞ then P(x) → ∞

2)

a_n\ \text{is negative}

then if x → -∞  then P(x) → -∞

and if x → ∞ then P(x) → -∞

I<u>f n is odd:</u>

1)

a_n\ \text{is positive}

then if x → -∞  then P(x) → -∞

and if x → ∞ then P(x) → ∞

2)

a_n\ \text{is negative}

then if x → -∞  then P(x) → ∞

and if x → ∞ then P(x) → -∞

Y_Kistochka [10]3 years ago
6 0
A polynomial with a positive leading coefficient will always be increasing, as x approaches infinity. Consider a polynomial with a positive leading coefficient and is degree 'n', where 'n' is an integer greater than zero. Differentiating the function tells us whether the function is increasing or decreasing. Since the coefficient of the first term of the derivative is positive (since 'n' and the coefficient is positive), the limit as x approaches infinity is positive infinity, as the highest degree is all that needs to be evaluated. Since the limit is positive, the function increases indefinitely.
Even if you differentiate once more (assuming n > 1), we find that the leading term still has a positive coefficient. This means that the limit as x approaches infinity, is once again, positive. This indicates positive concavity, thus, supporting the argument.

The same argument can be made to claim that polynomials with a negative leading coefficient approach negative infinity, as x approaches infinity.
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Geometry)) Find the value of x
Harlamova29_29 [7]

Answer:

\tt x=14

Step-by-step explanation:

\tt 6x+6=90

\tt 6x+6-6=90-6

\tt 6x=84

\tt \cfrac{6x}{6} =\cfrac{84}{6}

\tt x=14

~

8 0
2 years ago
Can someone please teach me how to do this? You can please do like 2 questions and please explain exactly how you got the answer
spayn [35]

All of these questions require one thing: trigonometric functions.

There are 3 main trigonometric functions, which can only be used on right triangles: sine, cosine, and tangent.

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

When trying to figure out what function to use, we always start by looking from the angle. Take problem a, for example. Looking from angle E, of which the value is not given, we have the side opposite and the side adjacent. Therefore, we should use the tangent function.

---The hypotenuse is always the longest side of the triangle. It is never considered the opposite or adjacent side.

Let's set up our function with the given information from problem a.

tan(x) = 9.7 / 5.2

---The tangent of an unknown angle is equal to the quotient of the opposite side and the adjacent side.

Now, solving for the value of x will require a calculator. We'll need to use what's called an inverse trigonometric function. Most calculators have these directly above the regular trigonometric functions, and the inverse functions are accessed using a "second" key.

---Ensure that your calculator is in degrees, not radians!

x = tan^-1(9.7 / 5.2)

x = 61.805 = 62 degrees

Next, let's take a look at problem b. This time, we're solving for a side length instead of an angle. But, we're still going to start by looking from our angle.


Looking from the 38 degree angle, we are given the adjacent side and an unknown hypotenuse. Therefore, we should use the cosine function.

cosine(38) = 53.1 / r

---The cosine of a 38 degree angle is equal to the quotient of 53.1 and an unknown hypotenuse, r.

Use your algebra skills to isolate the variable r.

r * cosine(38) = 53.1

r = 53.1 / cosine(38)

---From here, all you need to do is plug this into your calculator. Since we are solving for a side length (and given an angle), we are just using the regular trigonometric function buttons on the calculator.

r = 67.385 = 67.4 units

Hope this helps!

4 0
2 years ago
Which equations have a unit rate of change of 4.5 ? select 2 answers
Maurinko [17]

Answer:

Options A and C

Step-by-step explanation:

<u>To have a unit rate of change of 4.5 means to have the slope at 4.5</u>

A.  y = 62 + 4.5x  GOOD

B.  c = 4.5 + 3h - 1  WRONG

C.  c = 12 + 4.5h - 4.5  GOOD

D.  y = 3.5x + 1  WRONG

E.  y = 4.5  + 20x WRONG

Answer:  Options A and C

3 0
3 years ago
The highest point in Texas ,Guadalupe peak is 8749 feet high the highest point in California Mount Whitney is 14497 feet high. H
Inessa05 [86]
Just subtract 8749 feet from 14497 feet.

 14497 feet
-  8749 feet
----------------
     ?      feet
8 0
2 years ago
The graph of a proportional relationship passes through the points (15,3) and (5,y). Find y.
snow_tiger [21]
Y is equal to 1 because to change 15 into 5 you have to divide by 3. 15/3=5. So you do the same to the other coordinate. Divide 3 by 3 to get 1.
5 0
2 years ago
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