Which of the following rational functions is graphed below?
Answer:
do you have a picture for people to see
20. Give an example of a function from N to N that is a) one-to-one but not onto. b) onto but not one-to-one. c) both onto and one-to-one (but different from the identity function). d) neither one-to-one nor onto.
Answer:
Step-by-step explanation:
a) To provide an example of a function N → N that is one-to-one but not onto.
Suppose [tex]f:N\to N[/tex] to be [tex]f(n)=n^2[/tex]
Then; [tex]\text{a function } \ f: A \to B\ \text{is one-to-one if and only if } f(a) = f(b) \implies a = b \ for \ a, b \ \epsilon \ A.[/tex]
[tex]\text{a function } \ f: A \to B\ \text{is onto if and only if for every element } b \ \epsilon \ B \\ \text{there exist an element a} \ \epsilon\ A \ such \ that f(a) = b}[/tex]
Now, assuming [tex]a \ \Big {\varepsilon} \ N \& \ b \ \epsilon \ N;[/tex]
Then [tex]f(a) = f(b)[/tex]
[tex]a^2 = b^2 \\ \\ a = b[/tex]
The above function is said to be one-to-one
[tex]\text{it is equally understandable that not every natural number is the square of a natural number}[/tex]e.g
2 is not a perfect square, hence, it is not regarded as the image of any natural no.
As such, f is not onto.
We can thereby conclude that the function [tex]f(n) = n^2[/tex] is one-to-one but not onto
b)
[tex]Suppose f: N \to N[/tex] be
[tex]f(n) = [n/2] \\ \\ For \ n =1, f(1) = [1/2] = [0.5] = 1 \\ \\ For \ n=2 , f(2) = [2/2] = [1] = 1[/tex]
It implies that the function is not one-to-one since there exist different natural no. having the same image.
So, for [tex]n \epsilon N[/tex] , there exists an image of 2n in N
i.e.
[tex]f(2n) = [2n/2] = [n] = n[/tex]
Hence, the function is onto
We thereby conclude that the function [tex]f(n) = [n/2] \text{ is onto but not one-to-one}[/tex]
c)
[tex]let f: N\to N[/tex] be [tex]f(n) = \left \{ {{n+1, \ if \ n \ is \ even } \atop n-1 , \ if \ n \ is \ odd} \right.[/tex]
So, if n, m is odd:
Then:
[tex]f(n) = f(m) \\ \\ n-1 = m-1 \\ \\ n = m[/tex]
Likewise, if n, m is even:
Then;
[tex]f(n) = f(m) \\ \\ n+1 = m+ 1 \\ \\ n = m[/tex]
The function is then said to be one-to-one.
However, For [tex]n \epsilon N[/tex] and is odd, there exists an image of [tex]n - 1[/tex]that is even;
[tex]f(n - 1) = n -1 + 1 =n[/tex]
For [tex]n \epsilon N[/tex] and is even, there exists an image of [tex]n + 1[/tex]that is odd;
[tex]f(n - 1) = n +1 - 1 = n[/tex]
where(; implies such that)
Hence, this function is said to be onto.
We can therefore conclude that the function [tex]f(n) = \left \{ {{n+1, \ if \ n \ is \ even } \atop n-1 , \ if \ n \ is \ odd} \right.[/tex] is both onto and one-to-one.
d)
Here, to provide an example where the [tex]f:N \to N[/tex] is neither one-to-one nor onto.
SO;
Let [tex]f : N \to N[/tex] is defined to be [tex]f(n)=0[/tex]
Then, since every integer has the same image as zero(0), the function is not one-to-one.
Similarly, the function is not onto since every positive integer is not an image of any natural number.
We, therefore conclude that, the function [tex]f(n)=0[/tex] is neither one-to-one nor onto.
Can someone please solve this for me?
107 + 12
Show your work and I'll give brianliest (I know the answer i just need someone to show their work on how to get it)
A basketball player makes 85% of her foul shots. If 10 of her foul shots are randomly selected, what is the probability that 8 of them are successful shots?
0.06
0.28
0.85
0.98
Answer: 0.28
Step-by-step explanation: Reviewed my quiz, got you covered
There is a sale on sneakers. The price tag says $150. There is a 25% off sale. What is the final price with the discount? USE AN EXPRESSION.
Expression: ___________________
Answer:_______________________
Answer:
Step-by-step explanation:
Find the third degree polynomial function that has an output of 40 when x=1, and has zeros −19 and −i?
Answer:
[tex]f(x) = (x + 19)(x^2 + 1)[/tex]
Step-by-step explanation:
Complex numbers:
The following relation is important for complex numbers:
[tex]i^2 = -1[/tex]
Zeros of a function:
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
Has zeros −19 and −i
If -i is a zero, its conjugate i is also a zero. So
[tex]f(x) = a(x - (-19))(x - (-i))(x - i) = a(x+19)(x+i)(x-i) = a(x+19)(x^2 - i^2) = a(x + 19)(x^2 + 1)[/tex]
Output of 40 when x=1
This means that when [tex]x = 1, f(x) = 40[/tex]. We use this to find the leading coefficient a. So
[tex]f(x) = a(x + 19)(x^2 + 1)[/tex]
[tex]40 = a(20)(2)[/tex]
[tex]40a = 40[/tex]
[tex]a = 1[/tex]
The polynomial is:
[tex]f(x) = (x + 19)(x^2 + 1)[/tex]
charlie's puppy max weighs 10 pounds. How many ounces does Max weigh?
Answer:
160 ounces
Step-by-step explanation:
16 ounces=1 pound
10x16=160
there are 4 red balls in a bag and 8 yellow balls a ball is drawn random from the bag find the probability of not red ball
Answer:
2/3
Step-by-step explanation:
There are 4 red balls and 8 yellow balls.
Therefore, there are total 12 balls in the bag.
n(S) = 12
Let A be the event when the ball drawn is not a red ball.
The balls which are not red will be yellow balls and there are 8 yellow balls so,
n(A) = 8
Probability that the ball drawn randomly from the bag is not a red ball,
p(A) = n(A) / n(S)
= 8/12
= 2/3
Therefore, the probability of the ball drawn randomly is not a red ball is 2/3.
Can a triangle have the following side lengths? Explain.
5 feet, 2 feet, 10 feet
Answer:
No, this can not be a triangle because if you use the Pythagorean theorem 5 squared plus 2 squared doesn't equal 10 squared.
Step-by-step explanation:
You take 5 squared and 2 squared and add them, you then find the square root and that should equal 10, if not its not a triangle.
Windsor the dog ate 4 3/4 snack bones each day for a week . How many bones did Windsor eat that week ?
Answer:
4*3/4* 7=21 bones per week
Answer:
= 4 ¾ × 7
= 33.25 snack bones
Please answer this correctly without making mistakes
Answer:
w-(v+4)
Step-by-step explanation:
please give brainliest
Which of the following is not represented in the
image below?
8
O Line segment CD
O Line BC
O Ray BC
O Point B
Answer:
Line segment CD and Line BC are not represented.
Step-by-step explanation:
Line segment CD is not represented because a line segment is a portion of a line that has 2 distinct end points.
Line BC is not represented because a line is a straight path that has no beginning nor an end
Ray BC is represented because a ray is a part of a line which has one end point and extends infinitely in one direction.
Point B is represented because we can see a dot at B indicating that B is a point.
Need help Arc angles
can someone please help me i cant fail this
y = 700(1.05)^x,
plug in x=2
700(1.05)^2
= 700(1.05 times 1.05)
= 700(1.1025)
= 771.75
What is the answer to this
I'm lost on this please help
Answer:
Y=1/4x+33/4
Step-by-step explanation:
Y=1/4x+b
9=1/4(3)+b
9=3/4+b
8.25=33/4=b
Y=1/4x+33/4
Every week William collects a few pounds of plastic bags to recycle. The graph below shows the total number of pounds of plastic bags (y) that William collected in a certain amount of time (x), in weeks:
What would most likely be the total amount of plastic, in pounds, William would collect in 10 weeks?
340 pounds
400 pounds
440 pounds
540 pounds
Answer:
A. 340 lbs
hope this helps
Answer:
440
Step-by-step explanation:
Y=Mx+b
y=40x+40
y=40(10)+40
y=400 + 40
y=440
Which equations can be best solved with the square root method?
Select each correct answer.
x2−100=0
(x−6)2=25
x2−11x=−28
x2−10x+24=0
Answer:
The first two equations.
Step-by-step explanation:
The first equation:
x² - 100 = 0
x² = 100
√x² = √100
x = ±10
x = 10 or -10
Second equation:
(x - 6)² = 25
√(x - 6)² = √25
x - 6 = ±5
x - 6 = 5 or x - 6 = -5
x = 11 or 1
It seems that for the other two equations, you have to complete the square and factor them out.
-4x - 4(6x-14) +8(6x-10) - (20x -18)
Answer:
I believe it is -6
Step-by-step explanation:
If FX) = 3x+6, which of the following is the inverse of Fx)?
A. F1(x) = 6 - 3x
B. F1(x) = 3x - 6
C. F'(x) = x - 6 / 3
D. F'(x) = x - 3 / 6
Answer:
C. F'(x) = x - 6 / 3
Step-by-step explanation:
[tex]y = 3x + 6[/tex]
[tex]x = 3y + 6 \\ x - 6 = 3y + 6 - 6[/tex]
[tex] \frac{x - 6}{3} = \frac{3y}{3} [/tex]
[tex]y = \frac{x - 6}{3} [/tex]
[tex]f1 = \frac{x - 6}{3} [/tex]
3. A deli sells small, medium, and large box lunches. Each can of soda costs $1 and each bag of chips costs $1. Each sandwich costs s dollars. Some customers buy box lunches, and some customers buy items separately. Use this and the information below to solve Parts A, B, and C.
• Michelle buys 6 sandwiches and 2 sodas. Her total cost is 6s+ 2.
• Beyunka buys 6 small box lunches. These box lunches include 1 sandwich, 1 soda, and 1 bag of chips. Her total cost is 6(s + 2).
Duff buys 3 medium box lunches. These box lunches do not include soda. His total cost is 3(2s + 3).
3. PART A: Each medium box lunch purchased by Duff contains two sandwiches and three bags of chips. If sandwiches cost $7.75, what is Duff's total cost?
Answer:
55.50
Step-by-step explanation:
2(7.75) = 15.5
15.5+3 = 18.5
3(18.5) =55.5
$55.50
Determine the perimeter of a rectangle feet
Step-by-step explanation:
2l+2w=perimeter
L is Length
W width
Answer:
24ft
Step-by-step explanation:
it said its right
if a football team played 160 matches and won 65 percent of them,how many matches did it win
Answer:
65 x 160 / 100 = 104
Step-by-step explanation:
slove this plzzz plzzz
Answer:
an equilateral triangle have equal angles and equal sides.
so, side x and side bc are 12.
Answer:
It's going to be 12, so is the other size.
Step-by-step explanation:
You can see that in each corner, it shows the triangle is the same, which means it is equilateral, so the answer is 12 :D
In a small group, the ratio of club members to non-members is 6 to 5. What is the ratio of non-members to the total group size?
A. 6 to 5
OB. 5 to 6
C. 11 to 5
D. 6 to 11
O E. 5 to 11
The ratio of non-members to the total group size is to be considered as the option C. 11 to 5
Calculation of the ratio:Since
In a small group, the ratio of club members to non-members is 6 to 5.
So, the total members should be
= 6 + 5
= 11
Now the ratio be like 11 to 5
Hence, the option c is correct.
Learn more about ratio here: https://brainly.com/question/13021566
If 4x - 3y = -18 and 6x + 7y = -4, then what is the value of y?
Answer:
y = 2
Step-by-step explanation:
4x - 3y = -18, then 4x = 3y - 18, x = (3y - 18)/4
6x + 7y = -4
substitute for x:
6((3y - 18)/4) + 7y = -4
(18y - 108)/4 + 7y = -4
4.5y - 27 + 7y = -4
combine like terms:
11.5y = 23
y = 2
check:
x = (3(2) - 18)/4 = -12/4 = -3
6(-3) + 7(2) = -4
-18 - 14 - -4
-4 = -4
so y = 2 is correct
If 40% of the voters who responded are over 40 years old, how many voters responded in all?
A. 120
B. 88
C. 80
D. 68
20. Find the mean, median, and mode for the following
data set:
83 98 22 89 99 98
Answer:
GOT U
Step-by-step explanation:
Mean = 81.5
Median =93.5
Mode = 98
If y= 12x + 7 were changed to y = 12x + 2, how would the graph of the new
function compare with the original?
A. It would be less steep.
B. It would be steeper.
C. It would be shifted down.
D. It would be shifted up.
Answer:
C. It would be shifted down.
General Formulas and Concepts:
Algebra I
Reading a Cartesian Plane
Functions
Graphing
Coordinates (x, y)
The y-intercept is the y value when x = 0. Another way to reword that is when the graph crosses the y-axis.
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
[Original Function] y = 12x + 7
[Transformed Function] y = 12x + 2
Step 2: Identify
Compare functions to general form.
[Original Function] Slope m = 12, y-intercept b = 7
[Transformed Function] Slope m = 12, y-intercept b = 2
Step 3: Compare
We see that they both have the same slope m of 12, so A and B can be eliminated as the slopes don't change and therefore would not be steeper or less steep.
Now comparing the y-intercept b's, we see that the original function has a bigger b than the transformed function. This tells us that the original function will start higher than the transformed function.
We can also graph both equations and see what happens to the original equation.
∴ the answer would be C. It would be shifted down.
Tanisha scored 31 out of 35 points on a recent math quiz. The percent that Tanisha answered
correctly is closest to
1) 86%
2) 89%
3)91%
4)93%
Answer:
2) 89%
Step-by-step explanation: