Power Function:
Exercise: Recognize and analyze the graph of the power function as the exponent "n" and the coefficient "a" vary

1. Consider a positive exponent power function
A) Describe the graph of the function when n is even, for this you must attach an image of the graph of the function that meets these conditions.
B) Describe the graph of the function when n is odd, for this you must attach an image of the graph of the function that meets these conditions.
C) Describe what happened when the coefficient a is positive and also when it is negative. Is there any change in the graph?
D) Describe what happened when the coefficient a increases or decreases. What happens to the graph of the function?

2. Consider a negative exponent power function
A) Describe the graph of the function when n is even, for this you must attach an image of the graph of the function that meets these conditions.
B) Describe the graph of the function when n is odd, for this you must attach an image of the graph of the function that meets these conditions.
C) Describe what happened when the coefficient a is positive and also when it is negative. Is there any change in the graph?
D) Describe what happened when the coefficient a increases or decreases. What happens to the graph of the function?

Answers

Answer 1

Problem 1

Part A

If n is even, then we have a "parabolic" shape going on. I put that in quotes because if n = 2, then we have a true parabola; however, if n is even and larger than 2, then we have a curve that looks like a parabola, but it's not exactly a perfect parabola. All of these curves have in common that the end behavior is the same for the left and right sides.

Consider the example where a = 1 and n = 2. This means

y = a*x^n

turns into

y = 1*x^2

which is the same as

y = x^2

This produces the parent parabola curve. This curve opens upward.

I recommend using Desmos to graph y = a*x^n, where the 'a' and n are parameters set up. Check out the screenshot below.

---------------------

Part B

If n is odd, then we'll get something that looks like a cubic curve. If n = 3, then we get a cubic curve. If n is odd and n > 3, then we get something that looks like a cubic curve, but it's not exactly this perfect cubic.

If we let a = 2 and n = 3, then y = a*x^n becomes y = 2x^3. The graph of which is below.

---------------------

Part C

If a > 0 then the curve is like the previous examples shown earlier.

If a < 0, then we will reflect those given earlier curves over the horizontal x axis. An example is shown below using y = -x^2. This time we have a = -1 and n = 2. In other words, I reflected the example in part A over the x axis.

---------------------

Part D

As 'a' increases, then the graph gets more narrow. It also gets vertically stretched. Consider the example of going from y = 1x^2 to y = 3x^2 as shown below.

As 'a' decreases, then the process is done in reverse: the curve gets more flatter and wider horizontally. We consider the curve to be vertically compressed or squished. So we'd go from y = 3x^2 to y = 1x^2 as an example.

============================================================

Problem 2

Part A

For all of problem 2, we'll only consider negative values of n. We want n to be even, so let's say n = -2. Furthermore, let's say a = 2.

This means y = ax^n becomes y = 2x^(-2) which is the same as y = 2/(x^2)

The curve we get is really two separate pieces. There's a gap or disconnect at x = 0 because of a division by zero error. One piece of the curve is always increasing, while the other piece is always decreasing.

---------------------

Part B

Since we want n to be odd and negative, let's say n = -1. We'll keep a = 2 the same as before.

That means y = ax^n becomes y = 2x^(-1) as shown in the diagram below. What we have is a hyperbola. This is a disconnected set of two curves that collectively entirely define this function in a visual sense. Note the gap when x = 0 due to the division by zero error.

Recall that y = 2x^(-1) is the same as y = 2/x

Again, I'm using Desmos to generate each of these graphs.

Similar to part A, the two pieces are disconnected. This curve is known as hyperbola. It's always increasing if a < 0, and it's always decreasing when a > 0.

---------------------

Part C

If 'a' is positive, then the graph of y = 2/(x^2) is entirely above the x axis (aka everything is positive). On the flip side, if 'a' is negative, then everything swaps to being negative. That will reflect the curve over the x axis to get what you see in the example below. We have a = -2 and n = 2.

---------------------

Part D

As 'a' increases, this means the graph spreads out. If 'a' decreases, then it gets more compressed.  

An example is shown below going from y = 1/x to y = 3/x which shows expansion going on (reverse it to get a compression).

============================================================

Once again, the screenshots are shown below as examples.

Power Function:Exercise: Recognize And Analyze The Graph Of The Power Function As The Exponent "n" And
Power Function:Exercise: Recognize And Analyze The Graph Of The Power Function As The Exponent "n" And
Power Function:Exercise: Recognize And Analyze The Graph Of The Power Function As The Exponent "n" And
Power Function:Exercise: Recognize And Analyze The Graph Of The Power Function As The Exponent "n" And

Related Questions

Help thank you………………

Answers

Answer:

it is too easy I will answer it soon.

11. The sales tax rate for the state of Washington was 8.4%. What is the final cost of a $5,700 car in Washington,
including tax?
$

Answers

Answer:

$5853.60

Step-by-step explanation:

8.4% of $5400 = $453.60

$453.60 + $5400 = $5853.60

Area of the Shaded Region rectangle within reactanlge
Find the area of the shaded region with the following measurements:

Answers

Answer:

132

Step-by-step explanation:

First you need to find the area of both regions (shaded and not shaded)

To find the shaded regions area multiply length by width

20 x 8 = 160

Then find the area of the unshaded region

7 x 4 = 28

Finally subtract the unshaded region from the shaded region

160 - 28 = 132

find out the things that can be purchased between rupees 500 to rupees 100 for your house ?

Answers

We can buy small vases,Flower pots for our houses.

[tex]\sf\orange{Hope \: it \: helps \: please \: mark \: me \: as \: brainliest!}[/tex]

7 + (-24) / 8 + 4 (-2) =

Answers

Answer: 0

Step-by-step explanation:

7+(-24)/8+4(-2 )= 7-24/8+4(-2) = -17/8-8 = -17/0 = 0

ILL GIVE BRAINLIEST

evaluate the expression. 2•7(3^2)/3

Answers

Answer:

[tex] \frac{7 \times {3}^{2} }{3} \\ \frac{7 \times 3 \times 3}{3} \\ = 7 \times 3 = 21 \\ thank \: you[/tex]

The answer is 43
7(3^2) / 3 gives you 21
21 X 2 give you 42

Write an equivalent expression in standard form for
(5x + 4)(7x+ -12x + 27).


Answers

Answer: -25x² + 115x + 108

Concept:

When encountering questions that ask for simplifying polynomial expressions, using the method FOIL would be easier:

First, which means multiplying the first terms together;Outer, which means that we multiply the outermost terms when the binomials are placed side by side;Inner, which means multiply the innermost terms together;Last, which means multiplying the last term in each binomial together;

Solve:

Given

(5x + 4) (7x + (-12x) + 27)

Combine like terms in the parentheses

=(5x + 4) (7x - 12x + 27)

=(5x + 4) (-5x + 27)

Expand parentheses and apply the FOIL method

=-25x² + 135x - 20x + 108

Combine like terms

= [tex]\boxed {-25x^2+115x+108}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex]\boxed {\boxed {\sf -25x^2+115x+108}}[/tex]

Step-by-step explanation:

We are asked to find an equivalent expression for (5x + 4)(7x+ -12x + 27). Note that we are multiplying 2 polynomials.

[tex](5x + 4)(7x+ -12x + 27)[/tex]

Notice that the second polynomial has like terms. There are 2 terms with an x (7x and -12x) and we can combine them.

[tex](5x + 4)[(7x+ -12x) + 27][/tex]

[tex](5x + 4)[(-5x) + 27][/tex]

[tex](5x+4)(-5x+27)[/tex]

Now we are multiplying 2 binomials. Therefore, we use the FOIL method. We multiply the First terms, the Outside terms, the Inside terms, and the Last terms.

First:  5x * -5x = -25x²Outside: 5x * 27 = 135x Inside: 4* -5x = -20x Last: 4 * 27=108

[tex]-25x^2+135x-20x+108[/tex]

Notice there are 2 terms with an x ( 135x and -20x). They are like terms and can be combined.

[tex]-25x^2+(135x-20x)+108[/tex]

[tex]-25x^2+115x+108[/tex]

The equivalent expression in standard form is -25x²+115x+108

Which set of ordered pairs represents a function?

{(3,6), (3, 1), (9,0), (2, 2)}

{(2,-5), (-3, 6), (-1, -8), (-3,-4)}

{(4, -7), (-2, -1), (-7,4), (9, -1)}

{(3,8), (-2,-9), (1,4), (1,9)}

Answers

Answer:

{(4, -7), (-2, -1), (-7,4), (9, -1)}

Step-by-step explanation:

Every other set of ordered pairs has an x-value that has more than one y-value. This is against the rules of a function. Therefore, {(4, -7), (-2, -1), (-7,4), (9, -1)} represents a function.

pleaseeeeee solve this!

Answers

Answer:

C

Step-by-step explanation:

One graph line is equal to 10km and there is 2 graph lines between Red Bank and Belleville.

Okay umm I’m not even sure if I read the problem correctly but I would go with second option and say it’s 10km

An elevator at a construction site has a maximum capacity of 3325 pounds. If the elevator operator weighs 225 pounds and each cement bag weighs 75 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

Answers

answer: 41

3325 - 225 = 3,100
3,100 / 75 = 41.3 but you can’t take .3 bags so you round down to 41

The solution to 12x = 36 is x =___. (Only input whole number) Numerical Answers Expected! Answer for Blank 1:

Answers

Hi ;-)

12x = 36

x = 36 : 12

x = 3

Hey there! I'm happy to help!

We see that an unknown number x multiplied by 12 is equal to 36. How do we find this number? Well, you can simply go backwards and divide 36 by 12, and this will give us our answer.

36÷12=3

Another way you can think about this is dividing both sides of the equation by 12, which isolates our x.

12x=36

12x÷12=36÷12

x=3

Have a wonderful day and keep on learning! :D

A store advertises a sale on t-shirts. The advertised price is four t-shirts for $48. Write and solve an equation to find the cost of one t-shirt.

a.) $8
b.) $12
c.) $16
d.) $48

Answers

4 tshirts = $48

( Divide by 4 )

1 tshirt = $12 -b.)


Pls give me a brainliest if this helped thx

22b^9 divided by -2b^5

Answers

Answer:

-11 bytes4Step-by-step explanation:

please solve its due

Answers

Answer:

2118+3391+4785+6354= 16648

Step-by-step explanation:

Find the value of x
2,8,9,7,6x ; the mean is 6

Answers

Answer:

x=2/3

Step-by-step explanation:

The mean is just the average of all the terms. Therefore, you can set up an algebraic expression to solve for x.

[tex]\frac{2+8+9+7+6x}{5} =6[/tex]

[tex]2+8+9+7+6x=30\\26x+6x=30\\6x=4\\x=4/6=2/3\\x=2/3[/tex]

simplify given
[tex] \sin3 \alpha \div \sin \alpha + cos \alpha + cos3 \alpha \div cos \alpha - sin \alpha [/tex]

Answers

Step-by-step explanation:

Hey there!

Please see attached picture for your answer.

Hope it helps!

Can you help me please??

Answers

Answer:

either a or c sry

Step-by-step explanation:

abhivardhansinghrathore7979​

Answers

Answer:

hlo

Step-by-step explanation:

which Id I s ths and if u needs we can play t or d join eew-vtej-rxt

Answer:

thanks for the point back

Step-by-step explanation:

thanks

There are □terms in the sequence 1, 3, 9, 27, 81, 243, .... 6561

Answers

Answer:

There are(2) terms in sequence1,3,9,27,81,243...6561

Step-by-step explanation:

1,3,9,27,81,243,729,2187,6561

There are 8 terms in the sequence 1, 3, 9, 27, 81, 243, .... 6561.

To determine the number of terms in the given sequence, we can observe that each term is obtained by multiplying the previous term by 3. Starting with the first term, which is 1, we can continue this pattern to find subsequent terms.

1 * 3 = 3

3 * 3 = 9

9 * 3 = 27

27 * 3 = 81

81 * 3 = 243

243 * 3 = 729

729 * 3 = 2187

2187 * 3 = 6561

As we can see, the sequence follows a pattern of multiplying each term by 3. In total, we have gone through 8 terms to reach 6561.

To learn more about sequence click on,

https://brainly.com/question/29153938

#SPJ2

(x3)(x-5)
Fududeey
X=2

Answers

Answer:

-18 is the right answer..

Benchmark of 6/10, how do I get this worked out

Answers

Answer:

0.60 or 60% is the answer!

Step-by-step explanation:

Hope I helped

100 10 times as much as ___ of

Answers

Answer:

1 thousand

Step-by-step explanation:

1 ten = 10 x 1 one (Read, as “1 ten is 10 times as much as 1 one.”) 1 hundred = 10 x 1 ten (Say, “1 hundred is 10 times as much as 1 ten.”) 1 thousand = 10 x 1 hundred (Say, “1 thousand is 10 times as much as 1 hundred.”)i hope im right

compute the absolute value and the conjugate of z = (1 + i) ^ 6​

Answers

Answer:

z = (1 + i)6 =³√2(cos π4+ isinπ4)´6= 8 µcos3π2+ isin3π2)¶= −8i. Hence |z| = 8 and ¯z = 8i. z = (1 + i)

I think I am not real sure

In polar form, we have

[tex]1+i = \sqrt2 e^{i\pi/4}[/tex]

Then by DeMoivre's theorem,

[tex](1+i)^6 = \left(\sqrt2\right)^6 e^{i\,6\pi/4} = 2^3 e^{i\,3\pi/2} = -8i[/tex]

Then

[tex]|z| = |-8i| = \boxed{8}[/tex]

and

[tex]\bar z = \overline{-8i} = \boxed{8i}[/tex]

Which expression is equivalent to 8(6g)?

Answers

Answer:

8(6g) = 48g

I hope I helped you^_^

discoverings of marie curie​

Answers

Answer:

Marie won the 1911 Nobel Prize in Chemistry for her discovery of the elements polonium and radium, using techniques she invented for isolating radioactive isotopes. Under her direction, the world's first studies were conducted into the treatment of neoplasms by the use of radioactive isotopes.

Basically, she discovered new elements and one of them is radiation which is used world-wide for cancer and other things

Step-by-step explanation:

what's
the answer?????

Answers

9514 1404 393

Explanation:

Apparently, you're to show this is an identity.

  [tex]\dfrac{\tan^2A}{\tan A-1}+\dfrac{\cot A}{1-\tan A}=1+\sec A\csc A\\\\\dfrac{\tan^2 A-\dfrac{1}{\tan A}}{\tan A-1}=\\\\\dfrac{\tan^3 A-1}{(\tan A)(\tan A-1)}=\\\\\\\dfrac{\tan^2 A+\tan A+1}{\tan A}=\\\\1+\dfrac{\sec^2 A}{\tan A}=\\\\1+\dfrac{1}{\cos A}\cdot\dfrac{1}{\sin A}=1+\sec A\csc A[/tex]

find the length of BE BC=3x+47 DE=10 BD=x+27 CE=x+26

Answers

Answer:

B____C____D_____E

BC+ CE = BD + DE

(3x+47) + (x+26) = ( x+27) + (10)

4x + 73 = x + 37

4x – x = 37 – 73

3x = ‐ 36

x = – 36/ 3 —> x = 12

BC = 3x + 47 = 3(-12) + 47 = - 36 + 47 = 11

BD = x+ 27 = –12+27 = 15

CE = x + 26 = –12+26= 14

So;

BE = BD+ DE = 15+ 10= 25

Or ;

BE= BC + CE = 11+ 14 = 25

I hope I helped you^_^

Plz help ASAP need fast plz will mark Brainlyist

Answers

Answer:

The correct answer is the third one. CIRCUMFERENCE

What is the correct clases for this drugs

‏Compazine
heelp me please

Answers

Answer:

It is a addiction XD

Step-by-step explanation:

Bsgsgwgwggwgwfeffefecrcr

Convert this rational number
to its decimal form and round
to the nearest thousandth.
1/6

Answers

Answer: 0.166

Step-by-step explanation:

Converting to a decimal:

1/6 = 0.1666 (1 divided by 6 - long division)

Rounding:

0.1666 to the nearest thousandth = 0.166

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