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for fucks sake cphill dont answer the question

I actually got the end behavior right lol i just drew it wrong on here >.< I had written down correctly on paper and didn't realize I had switched them up on here.

Are you trying to solve those questions before sending them here?

here's a method for finding end behaviors:

When we have a polynomial P(x)=a_n*xⁿ+...+a₀ and we want to find the end behaviors of the polynomial, we can instead find the end behaviors of the polynomial a_n*xⁿ. The end behaviors will stay the same.

for example: if the polynomial is 2x⁴+x³+1 and we want to find the end behaviors we can replace the polynomial with the polynomial 2x⁴ and find the end behaviors for this polynomial instead.

PLEASE try solving this question, at least try to solve the end behavior part.

-3x^2 + 2x  -  3   =  0

a  = -3     b   = 2      c   =  -3

Using the Quadratic Formula

x  = [  - b ±√ [ b^2 - 4ac]  ] /  [ 2a]  =

[ -2 ±√ [ 2^2 - 4(-3)(-3) ] ] / [ 2 * -3 ]  =

[ -2 ±√ [ 4 - 36] ] / [ -6]  =

[ -2 ±√-32 ] / [ -6]  =

[-2 ±√ [ (-1)(16)(2) ] ] / -6

[-2 ±4i√2 ] / -6  =

[ -1 ± 2i√2 ] / -3  =

[ 1 ±2i√2 ] / 3   ⇒   "B"

For the second one the distance  is  √[23^2  - 12^2 ]  = √385  =  19.6 ft   ...correct  !!!

I just answered this yesterday

Apply the rational root theorem

\(\text{let }p(x) = a_0 + a_1 x + \dots + a_n x^n\)

\(\text{then if }x = \dfrac{p}{q} \text{ written in lowest terms is a root of p(x), }\\ \text{it must be that p divides }a_0 \text{and that q divides }a_n\)

\(\text{here we have }a_0 = -5,~a_3=1\)

\(\text{the only possible p's are }\pm 1,~\pm 5\\ \text{and the only possible q's are }\pm 1\)

\(\text{thus the only possible rational roots are }\pm 1,~\pm 5 \\ \text{and we just have to try them all to see if any are actually roots.}\)

\(p(-1)=14, ~p(1) = 22,~p(5)=710,~p(-5)=430 \\ \text{i.e. none of these are in fact roots and thus p(x) is irreducible over the rational numbers}\)

Domain and range are correct  !!!!

Relative max occurs at ≈  (2.816, 1.089)

Relative min occurs at ≈ (1.184, - 1.089)

You have the end behavior almost correct, RP

As the function approaches + inf....the end behavior  is  - inf

As it approaches -inf.....the end behavior  is  + inf

Increasing intervals  [ where the function rises from left to right  ]  = (1.184, 2.816 )

Decreasing intervals [ where it  falls from left to right ] = (-inf, 1.184) U (2.816, inf )

Here's the graph :  https://www.desmos.com/calculator/mk1cbfvwvh

Is this all clear to you  ????

Correct !!!....positive inf on the left end......negative inf on the right end

positive then negative infinity?

Let's just look at this, RP : https://www.desmos.com/calculator/cb1kkobkfe

Can you answer this, now  ???

Thanks CPhill and Rom

tysm <3

x^2 + 36  = 0  subtract 36 from both sides

x^2  = -36       take both roots

x  = ±√ - 36  = ±√ [ (-1)(36) ]  = ± i * 6  =  ± 6i

[ Remember that   √ (-1)  =  i  ]

There are no solutions over the real numbers.

Over the complex numbers the two solutions are

x = +/- 6i

where i is the square root of -1

First one

a) End behavior -  negative infinity at the left end, positive infinity at the right end

b) Neither - it is not even because it is not symmetric to the y axis....to be odd....we could "flip" the fuction on either side of the y axis and it would have to mirror the other side...this is not true for this function

c) The lead coefficient is positive

Second one

a) End behavior  - negative infinity at both ends

b) Neither   -  not symmetric to the y axis

c) The lead coefficient is negative

Functions don't have to be either odd or even RP.  See below for example:

.

I am pretty sure you are right 

Melody clearly told you to do it yourself and you opened the last thread just 2 hours ago, why are you reposting? because you know cphill will answer your questions anyways?

Combine 'like' terms:

(3x^3  - x^3) + (-x^2 + 5x^2) + (4x) + (8-7)

2x^3 + 4x^2 + 4x +1        

\(x-(11+\sqrt[3]{13}) = 0 \\ x - 11 = \sqrt[3]{13} \\ \text{now cube both sides} \\ x^3-33 x^2+363 x-1331 = 13 \\ x^3-33 x^2+363 x-1318 = 0\)

I got beat to it haha

a^2 + b ^2  = c^2

(2)^2  + (12)^2 = c^2

4 +144 = c^2

148 = c^2

c = +- sqrt(148) = +-12.166