A function f is odd and f(x)=x^2 for all x>0. Sketch the graph of this function and then write the rule of this function as a single formula.
Answers
We will see that we have a piecewise function:
f(x) = x^2 for x > 0.f(x) = -x^2 for x ≤ 0.The graph can be seen at the end.
What is an odd function?
A function is odd when f(-x) = -f(x) for all the values of x in the domain of the function.
In this case, we know that:
f(x) = x^2 for x > 0.
Then, for the negative range, the sign must change (but the quadratic function is even). Then we define the function in the negative range as:
f(x) = -x^2 for x ≤ 0.
This is the odd function (a piecewise function) for the whole domain:
f(x) = x^2 for x > 0.f(x) = -x^2 for x ≤ 0.The graph of the piecewise function can be seen below.
If you want to learn more about piecewise functions, you can read:
https://brainly.com/question/3628123
Answer:
[tex]f(x) =\frac{x^3}{|x|}[/tex]
Step-by-step explanation:
Being an odd function means that [tex]f(-x) = -f(x)[/tex].
Graphically, it means the function will be symmetric across the origin.
So, the graph will have to look like the shown graph.
This graph looks quite similar to the graph [tex]f(x) = x^3[/tex], so we can use that as our parent function.
To get the graph to equal [tex]x^2[/tex] for x>0, we must divide [tex]x^3[/tex] by x.
However, this will simply result in the function [tex]f(x) = x^2[/tex].
If we divide by the absolute value of x however, the graph will look as desired.
Related Questions
Bill bought a certain food in which there are 300 calories in 100 g of that food. What is the number of calories in a 20 g portion of this food?
Answers
Answer:
60
Step-by-step explanation:
If there are 300 calories in 100g of Bill's food, then we can divide 5 on both sides to find the number of calories in a 20g portion of this food: 300/5=60 calories.
The distance between the school and a students house is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days
Answers
We have to convert 1km 875m into meter so 1875m. To maintain the balance we did it
Six day she goes home to school and school to home will (1875*12) meter **here 12 because she walk home to school and school to home
= 22500meter
We convert back into km and meter
So 22km and 500m
So she walked 22kilometer 500meter
this is really confusing pls help! :)
Answers
an= 3n+1
whats 1784 rounded off
Answers
Answer:
1780 is the best answer
Step-by-step explanation:
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE let
Answer:
Depends on which digit r you asking for
thousands: 2000
hundreds: 1800
tenths: 1780
units: 1784
20 x 20 divided by 53 x z z=12
Answers
Answer:
90.5660377
Step-by-step explanation:
20×20÷53×12
400÷53×12
7.54716981×12
90.5660377
PLEASE HELP!! 20 POINTS!!
Answers
Answer:
yea
Step-by-step explanation:
Determine whether each of the following is a characteristic of a protist, fungus, or both. Unicellular Stationary Reproduces through spores Eukaryotic Cilia Autotrophic
Answers
Answer:
100% correct
Step-by-step explanation:
The properties of the protists differ from that of the fungi but they are both eukaryotic organisms and are unicellular.
What is a protist?
A protist is an organism that belongs to the Kingdom Protista. Fungus are the organisms that belong to the kingdom fungi.
Now, let us differentiate between the properties of the protists and the fungi;
Unicellular - both fungi and protists
Stationary - fungi
Reproduces through spores - fungi
Eukaryotic - both fungi and protists
Cillia - protists
Autotrophic - fungi
Learn more about protists: https://brainly.com/question/365923
2(x−3) = 2x + 15 how many solutions
Answers
Answer:
0
Step-by-step explanation:
2x-6=2x+15
2x-2x=15+6
0x/0=21/0
x=0
Find the volume of each sphere. Be sure to include appropriate units.
(Show your work)
Answers
Answer:
2145.5m^3
679.2yard
Step-by-step explanation:
v
[tex]volume \: of \: a \: sphere = \frac{4}{3}\pi \: r {}^{3} \\ when \: r = 8 \\ volume = \frac{4}{3} \times \frac{22}{7} \times 8 {}^{3} \\ volume = \frac{4}{3} \times \frac{22}{7} \times 8 \times 8 \times 8 \\ volume = \frac{4 \times 22 \times 512}{3 \times 7} \\ volume = \frac{45056}{21} \\ volume = 2145.5m {}^{3} \\ \\ for \: the \: second \: shape \\ volume = \frac{4}{3} \times \frac{22}{7} \times 5.5 {}^{3} \\ = \frac{4}{3} \times \frac{22}{7} \times 166.373 \\ = \frac{14641}{21} \\ = 697.2yard[/tex]
ANWSER ASAP RIGHT ANWSER GETS BARINLIST
A land snail, a clam, and an octopus all share this body structure:
Question 22 options:
gills
muscular foot
segmented bodies
jointed appendages
Answers
Answer:
A muscular foot
Step-by-step explanation:
hope this helps :)
square root (5/6)^2 help i need it fast
Answers
Simplify 5+1(-24)+(-21×1)
Answers
Which is the slope of the line that passes through the points (-3,-2) and (1,0)
Answers
Answer:
[tex]Slope = \frac{1}{2}[/tex]
Step-by-step explanation:
Let m be the slope of the line
We can calculate the slope m this way :
[tex]m = \frac{0-(2)}{1-(-3)} = \frac{2}{4 }= \frac{1}{2}[/tex]
Distributive Property to find (a+8)(a-3)
Answers
Answer:
[tex]a^{2} + 5a -24[/tex]
Step-by-step explanation:
For the distributive property, it is like multiplying each term by the other whole group.
For this problem we can set it up like this:
a(a-3) + 8(a-3) =
a^2 - 3a + 8a - 24 =
a^2 + 5a - 24
Simplify the expression
-6 +4x+ 9 -2x
Answers
Answer:
3 + 2x
Step-by-step explanation:
combine -6 + 9 = 3
combine 4x - 2x = 2x
Sara uses ribbon to make hair bows. The length of each ribbon Sara uses is represented by the line plot shown. What is the difference, in feet, between one of the pieces of ribbon that has the longest length and one of the pieces that has the shortest length?
Answers
1 foot because if you do 1 1/2 - 1/2 = 1
Tom makes $296.10 in 6 days. How much does he make in 5 days?
Answers
math problem: 296.10/6= 49.35
49.35*5= 246.75
can anyone help me with this math question
Answers
12 boys
hope it helps...!!!
This week Gap is offering 40% off all shirts and 50% off all shorts. Katie purchased 3 shirts for $25.65 and one pair of shorts priced at $22.80. About how much did Rebecca pay for the sweaters and jeans before tax?
Answers
The amount that Rebecca pay for the sweaters and jeans before tax for this case is $26.79
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
We're specified that:
Discount percent on shirts = 40%Discount percent on shorts = 50%The price of all 3 shirts = $25.65The price of one pair of shorts = $22.80Before taxing, the price to be paid is real price (marked on the items) - discount offered on them.
Now, we get:
Price of each shirt is assumingly same, and so as for both of shorts. The discounts would be same for all shirts, and the discount will be same for all shorts.
So sum of discounted price = discount on summed price.
Thus, discoutned price of 3 shirts = 40% discount on $25.65
= $25.65 - 40% of $25.65
We get this:
[tex]25.65 - \dfrac{25.65}{100} \times 40 = 25.65 \approx 0.6 = 15.39[/tex] (in dollars)
Similarly, we get:
Discounted price of shorts= $22.80 - 50% of %22.80 = 22.80 - 11.40 = 11.40 dollars
Thus, the total discounted price = discounted price of shirts and shorts= $15.39 + $11.40 = $26.79
Thus, the amount that Rebecca pay for the sweaters and jeans before tax for this case is $26.79
Learn more about percent here:
https://brainly.com/question/11549320
#SPJ1
Take look at this! Please see if you can figure it out. :(
Jeff Claims that the expression -6(2m-4) is equivalent to -12m-4. Is he correct? Explain your answer.
Thank you
Answers
if you do like terms you’d do
-6(2m) and -6(-4)
-6(2m)= -12m
-6(-4)=24
so he is wrong.
Can someone pls help ?!
Answers
Answer:
120 cubed inches
Step-by-step explanation:
5 x (3 x 8)
5 x 24
120
Answer:
Step-by-step explanation:
Volume of rectangular prism = lwh
= 8 * 3 * 5
= 120 cubic inches
-8x+19<-13 Solve inequalities
Answers
[tex]~~~-8x +19 < -13\\\\\implies -8x < -13 -19\\\\\implies -8x < -32\\\\\implies x > \dfrac{-32}{-8}\\\\\implies x > 4[/tex]
I need help, if you give answer ASAP I’ll reward a lot of points!!
Answers
Answer:
A = 31.875 inches squared
Step-by-step explanation:
Area of a parallelogram is bh
b = 12 and 3/4 is just 12.75 inches
h = 2 and 1/2 is just 2.50 inches
Multiply these together and you get the area,
A = (12.75)(2.50) = 31.875 inches squared
Answer:
31.875 (31.88 rounded)
Step-by-step explanation:
A =b x h
A =12.75 x 2.5
A = 31.875
----------------------
12.75 = 12 [tex]\frac{3}{4}[/tex]
2.5 = 2[tex]\frac{1}{2}[/tex]
The PE room at school has a variety of colored balls that can be used to play in the school yard. There are 16 red balls, 12 orange balls, 8 yellow balls, and 11 pink balls.
What is the probability that you are going to get a BROWN ball?
Answers
Answer:
0%
Step-by-step explanation:
There are no brown balls, so therefore it is impossible to get one.
Please help me with this!!!
Answers
Answer:
Its the first one.
Step-by-step explanation:
Just subtitue in values, the only one that works is the first one.
One factor of f (x ) = 5 x cubed + 5 x squared minus 170 x + 280 is (x + 7). What are all the roots of the function? Use the Remainder Theorem.
x = –4, x = –2, or x = 7
x = –7, x = 2, or x = 4
x = –7, x = 5, or x = 280
x = –280, x = –5, or x = 7
Answers
The roots of the function f(x) = 5x³ + 5x² - 170x + 280 are given by x = 4, x = 2 or x = -7
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that x + 7 is the root of 5x³ + 5x² - 170x + 280, hence:
(5x³ + 5x² - 170x + 280) / (x + 7) = 5x² - 30x - 40
Hence:
(5x³ + 5x² - 170x + 280) = (x + 7)(5x² - 30x - 40)
= 5(x² - 6x - 8)(x + 7)
= 5(x - 4)(x - 2)(x + 7)
The roots are at:
0 = 5(x - 4)(x - 2)(x + 7)
x = 4, x = 2 or x = -7
The roots of 5x³ + 5x² - 170x + 280 are x = 4, x = 2 or x = -7
Find out more on equation at: https://brainly.com/question/1214333
Which of the following is the correct factorization of the polynomial below?
x2-18
O A. (x+3)(x-6)
O B. (x-3)(x + 6)
O C. (x+3)(x2 - 4x+6)
D. The polynomial is irreducible.
Answers
Answer:
D. The polynomial is irreducible
Step-by-step explanation:
This polynomial is unfactorable. x² and 18 share no common factors. It is already in simplist form.
hope this helps :)
Can someone pleast help me with this
can you right a opening paragraph stateding why kids should do sports please, thanks!
Answers
Jaime rolls a number cube and spins a colored spinner. The spinner is divided into three equal sections. The tree
diagram shows all the possible outcomes that can occur.
Answers
Answer:
Step-by-step explanation:
The mountain in "The Negro Artist and the Racial Mountain" is considered as an obstacle for Negro artists who wish for others to recognize their work. This isn't just part of their job, but it's part of a racial dispute because of their color. Langston Hughes, the author, describes these Negro artists as very talented people. These are also people who believe they can make it big as artists, but they wish to be white to do so. Black artists think they can't be accepted as people, let alone artists. So the mountain in the essay represents a huge obstacle these people have to achieve. That obstacle is being accepted by everyone else, and that includes them looking past their color before appreciating their art.
Hope this helps you!!
If you answer this question right, I'll give you (BRAINLIEST)
A social studies test has 4 true-or-false questions. The following list shows the possibilities for a student's responses to these questions.
TTTT, TTTF, TTFT, TTFF, TFTT, TFTF, TFFT, TFFF, FTTT, FTTF, FTFT, FTFF, FFTT, FFTF, FFFT, FFFF
If a student randomly guesses for all four questions, what is the probability they get all four questions correct?
Enter your answer as a fraction, like this: 3/14
Answers
Answer:
1/16
Step-by-step explanation:
To find probiblity all you have to do is divide the number of events by the number of possible outcomes
There are 16 possible outcomes
and there is only 1` way that the student can get all 4 questions right
so the answer is: 1/16
Answer:
1/16
Step-by-step explanation:
Number of possible outcomes = 16
Only one set will be the correct option
P(getting all four questions correct) = 1/16