What is the domain and range of the function y = xn if n is an odd whole number? if n is an even whole number?

A. If n is odd, domain is (−∞,∞) and range is [0, ∞); if n is even, domain and range are both (−∞,∞).
B. If n is odd, domain and range are both (−∞, ∞); if n is even, domain is (−∞, ∞) and range is [0, ∞).
C. In both cases, domain is (−∞, ∞) and range is [0, ∞).
D. Domain and range in both cases is (−∞ , ∞ ).

Answers

Answer 1

Domain and range are the possible x and y values, a function can take.

For the given functions:

If n is odd, domain and range are both (−∞, ∞)If n is even, domain is (−∞, ∞) and range is [0, ∞)

Given that:

[tex]y = x^n[/tex]

When n is even.

Assume that [tex]n=2[/tex]

The equation becomes:

[tex]y =x^2[/tex]

See attachment for the graph of [tex]y =x^2[/tex].

From the graph, we can see that values of x extend to both sides of the x-axis.

So, the domain is: [tex](-\infty, \infty)[/tex]

However, the value of y starts from 0 and the curve opens upward. This means that y only take positive values.

So, the range is: [tex][0, \infty)[/tex]

When n is odd.

Assume that [tex]n =3[/tex]

The equation becomes: [tex]y = x^3[/tex]

See attachment for the graph of [tex]y = x^3[/tex].

From the graph, we can see that values of x and y extend to both sides of the x-axis and y-axis, respectively.

So, the domain is: [tex](-\infty, \infty)[/tex]

The range is: [tex](-\infty, \infty)[/tex]

Hence, option (B) is correct.

Read more about domain and range at:

https://brainly.com/question/1632425

What Is The Domain And Range Of The Function Y = Xn If N Is An Odd Whole Number? If N Is An Even Whole

Related Questions

calculate the median of 2,7,10,8,9,10,15



please do it step by step​

Answers

Answer: 9

Concept:

The median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.

In other words, the median of a set of data is the middlemost number or center value in the set.

Solve:

STEP ONE: Line up the terms in the set from least to most

Given = 2, 7, 10, 8, 9, 10, 15

Line up = 2, 7, 8, 9, 10, 10, 15

STEP TWO: Find the middlemost number

Given = 2, 7, 8, 9, 10, 10, 15

Since it is an odd set, therefore there should be the equal number of terms in the lower and higher half.

There are in total seven terms, therefore, the 4th term would be the middlemost, which is [tex]\boxed{9}[/tex].

Hope this helps!! :)

Please let me know if you have any questions

HELP ME PLEASE SOMEONE!!

Answers

Answer:

number 3

Step-by-step explanation:

number 3 the answer is the third one

Please help me!!!!
What is the midpoint of AB ?
B

Answers

Answer:

hope it helps you........

Step-by-step explanation:

The midpoint formula is

[tex] (\frac{x1 + x2}{2} ) \: and \: ( \frac{y1 + y2}{2} )[/tex]

Where (x1,y1) is one pair of the points and (x2,y2) is the other pair of points.

The points are

(-5,-4)

(-3,3) So the midpoint is

[tex]( \frac{( - 5 + ( - 3)}{2} )\: and \:( \frac{ - 4 + 3}{2} )[/tex]

Which gives us

[tex] - 4 \: and \: - 0.5[/tex]

So the midpoint is

(-4,-0.5)

write an equation that contains points (0, 4) and is perpendicular to x-3y=-12

Answers

X-3(4)=-2
x-12=-2
So ya add the -12 to both side and you get X=10

Answer:

y= -3x+4

Step-by-step explanation:

x+12=3y

(x+12)/3 = y

slope =

[tex] \frac{1}{3} [/tex]

the new slope = -3

Perpendicular slopes must be opposite reciprocals of each other:  m1 * m2 = –1

With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b

4 = -3×(0) + b

b= 4

so y= -3x+4

Find the inverse of the following


F(x)=-3/4x+6

Answers

Answer:

[tex] {f}^{ - 1} (x)= - \frac{4}{3} x + 8[/tex]

Step-by-step explanation:

[tex]f(x) = - \frac{3}{4} x + 6[/tex]

[tex]y = - \frac{3}{4} x + 6[/tex]

[tex]x = - \frac{3}{4} y + 6[/tex]

[tex] - \frac{3}{4} y + 6 = x[/tex]

[tex] - 3y + 24 = 4x[/tex]

[tex] - 3y = 4x - 24[/tex]

[tex]\boxed{\green{ {f}^{ - 1} (x)= - \frac{4}{3} x + 8}}[/tex]

What is the fractional equivalent of the repeating decimal 0 2 ?
O A i
O B.
O c.
OD.

Answers

What are the answers to A,B,C, and D

1^2 + 2^2 + 3^2 +.... + 28^2 + 29^2 + 30^2 = ......
Find the value
Thank you!

Answers

Step-by-step explanation:

The sum of consecutive squares is

[tex]1^2+2^2+\dots+n^2=\frac16n(n+1)(2n+1)[/tex]

Therefore

[tex]1^2+2^2+\dots+30^2=\frac16(30)(31+1)(2\cdot30+1) = 9455[/tex]

the math class has 9 girls and 14 boys. what is the ratio of girls to boys

Answers

Answer:

Girls:Boys

9:14

Hope it helps!!

The double of a number plus 12 is equal to its triple minus 5. What is the number? [tex]2x + 12 = 3x - 5[/tex] if I'm not wrong

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

17

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\2x + 12 = 3x - 5\\--------------\\\rightarrow 2x + 12 - 12 = 3x - 5 - 12\\\\\rightarrow 2x = 3x -17 \\\\\rightarrow2x -3x = 3x-3x - 17\\\\\rightarrow -x = - 17\\\\\rightarrow \frac{-x=-17}{-1} \\\\\rightarrow \boxed{x = 17}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

what is the simplified expression for-
HURRY PLEASE

Answers

Answer:

3/2

Step-by-step explanation:

you basically just simplify the exponents first, and then simplify from there.

PLEASE help answer these, thank you so much
I'll mark brainliest for best answers

Answers

Step-by-step explanation:

#1

6 × n + 15 = -42

6n + 15 = -42

6n = -42 - 15

6n = -57

n = -57/6

n = -19/3

#2

b + 3/2b + b + 45 + 2b - 5 + 90 = 540

b + 1.5b + b + 45 + 2b - 5 + 90 = 540

5.5b + 130 = 540

5.5b = 540 - 130

5.5b = 410

b = 410/5.5

b = 74.5

Angles are

b = 74.5

1.5(74.5) = 111.75

74.5 + 45 = 119.5

2(74.5) - 5 = 144

All cheeses in Blake's Grocery sell for no less than $3.95 per pound
but less than $4 per pound. List all possible cheese prices at the store
from least to greatest.

Answers

Answer:

3.95,3.96,3.97,3.98,3.99 i think lol

Step-by-step explanation:

5. Simplify the expression _49. O245 O 65 06 07​

Answers

Answer:

i think forth no.

Answer:

7

Step-by-step explanation:

49 is a perfect sqaure root cuz 7x7 = 49

please help it’s a ca!! will mark brainliest

Answers

Answer:

the first one: The coordinates of A' are (-2, 3)

and the last one: The coordinates of B' are (-2, 0) and the coordinates of C' are (2, -1).

Step-by-step explanation:

when you rotate a triangle counterclockwise by 90° you swap the numbers of the x and y coordinates.

like how the coordinates of B' were (0, 2) and became (-2,0) once the triangle was rotated.

The answer would be 1 and 4

o Step Word Problem
5. Stacey delivers newspapers. She earns $15 each week plus $2 for each customer on her route. Which
equation can she use to find c, the number of customers she needs to earn exactly $25 each week?
2x+18=25

Please help!!

Answers

Answer:

x = -5.5

Step-by-step explanation:

probaly wrong just a guess

Plssssss help me ASAP!!!!!

Answers

Answer:

6

Step-by-step explanation:

plug in 8 for all p so 4^2 = 16 / 8 x 3 ---> 2 x 3 = 6

What is the formula to get the volume of a cylinder

Answers

Answer:

V = π × r² × h

Step-by-step explanation:

All you need to do is multiply the base times the height and since the base is a circle whose formula is π × r², we get π × r² × h.

Answer: [tex]\bf \boxed{\bf V=\pi r^2 h}[/tex]

Step-by-step explanation:

[tex]\bf V=height \times (radius)^2\times \pi[/tex]

I need the answer to this question

Answers

Answer:

y = 3/4x + 19/2

Step-by-step explanation:

m = 3/4. point (-6,5)

Point slope form:

y-5=3/4(x- -6)

y -5 = 3/4x + 18/4. 18/4 = 9/2

Y = 3/4x + 9/2 + 5. 5 times 2 plus 9 over 2 = 19/2

y = 3/4x + 19/2

**Help fast!**

Solve for x: the quantity of x plus 20 over 2 = 3x

Answers

Answer:

x = 5

Step-by-step explanation:

(5) + 20/2 = 3(5)

Hope it helps

I agree X should equal five hope this helps

PLS HELP IM STUCK! WILL MARK BRAINLIEST! :)

Answers

Answer:

D

Step-by-step explanation:

We just need to plugin the points to the equation 5x + 2y = 7.

If we plugin x = 8 and y = -33/2 we can easily see that

5x + 2y = 5(8) + 2(-33/2) = 40 -33 = 7

So D is the right answer

Answer:

D[(8,-33/2)]

Step-by-step explanation:

Post In a bit

WILL MARK BRAINLY IF CORRECT
Solve the absolute value equation, |x| − 2 = 5.

A. x = 3 and x = −3
B. x = 7 and x = −7
C. x = −7 and x = 3
D. x = −3 and x = 7

Answers

B ,when it’s absolute the -7 becomes positive 7. You can also use photo math for that equation.

Answer:D

Step-by-step explanation:

Please help me!!
Solve for x and show your steps:

3x-ab=c

Answers

Answer:x=(c+ab)/3

Step-by-step explanation:

Add ab to c, then divide both sides by 3.

If AB = 2x + 6, BC = x + 10 and AC = 7x = 11
Find x.

Answers

Answer:

AB+BC=AC

2x+6 +x+10=7x

3x+16=7x

16/4=x

X=4


If (a, - 8) is a point on the graph of y=x + 6x, what is a?

Answers

First, [tex]y=7x[/tex] and when we plug in the point we get [tex]-8=7a\implies a=-\frac{8}{7}[/tex].

Hope this helps :)

pls, help The temperature of a city changed by −24 degrees Celsius over a 6-week period. The temperature changed by the same amount each week.


Part A: Write an expression to show the average change in the temperature of the city each week. (5 points)


Part B: Simplify the expression and explain, using words, what your answer means. (5 points)

Answers

Answer:

Step-by-step explanation:

The change over 6 week period is -24 degrees Celcius.

A.  -24/6

B . So in average every week  the temperature change is -24/6 = -4 degrees Celcius

x+ y + z=1
3x - y- z=7
2x - 2y - 4z = 52

Answers

https://core.ac.uk/download/pdf/48393503.pdf

Teachers divided students into groups of 3. Each group of 3 wrote a report that had 9 pictures in it. The students used 585 pictures altogether. How many students were there in all?

Answers

Each group used 9 pictures, first divide total pictures by pictures per group to find total groups:

585 / 9 = 65 total groups.

Each group had 3 students.

Multiply total groups by students per group:

65 x 3 = 195 total students

Answer: 195 students.

PLEASE HELP ASAP 10 points
What is the domain of the following relation:

{(-2, 0), (3, 5), (6, 10), (9, 11)}

Answers

-2, 3, 6, 9 (first numbers of a function. the last are the range.)
Domain: {−2,3,6,9} :):):):):):)

Consider these signed numbers and determine whether each product is positive or negative.
(-2/3) (524)
(4 5/9) (4/5)
(-6 3/4) (-7 1/11)

Answers

Answer:

1. negative. why: a negative multiplied by a positive will always be negative.

2. positive. why: a positive multiplied by a positive will always be positive.

3. positive. why: a negative multiplied by a negative will always be positive.

Step-by-step explanation:

hope this helps

Spider-Man worked 0.75 hour on math, 0.675 hour on writing, and 0.25 hour each on science and social studies. How many hours did he work in all?

Answers

Answer:

1.675

Step-by-step explanation:

Answer:

The answer is spider man work 1.675 hours

Step-by-step explanation:

0.75+0.675+0.25=1.675

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