The graph of F(x) can be compressed vertically and shifted to the right to produce the graph of G(x) . If F(x) = x ^ 3 , which of the following could be the equation of G(x) ?
Answers
Given:
The function is:
[tex]F(x)=x^3[/tex]
To find:
The function G(x) if the graph of F(x) can be compressed vertically and shifted to the right to produce the graph of G(x).
Solution:
The transformation is defined as
[tex]g(x)=kf(x+a)+b[/tex] .... (i)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
It is given that F(x) can be compressed vertically and shifted to the right to produce the graph of G(x). So, the value of k must be lies between 0 and 1, and a<0.
In option A, [tex]0<k<1[/tex] and [tex]a<0[/tex]. So, this option is correct.
In option B, [tex]0<k<1[/tex] and [tex]a>0[/tex]. So, this option is incorrect.
In option C, [tex]k>1[/tex] and [tex]a>0[/tex]. So, this option is incorrect.
In option D, [tex]k>1[/tex] and [tex]a<0[/tex]. So, this option is incorrect.
Therefore, the correct option is A.
Related Questions
Each of the digits 3, 4, 6, 7, 8, and 9 is used once and only once to form a six-digit integer. What is the largest six-digit multiple of 4 that can be formed
Answers
Answer:
987436Step-by-step explanation:
The number is divisible by 4 if the number formed by the last two digits is divisible by 4.
Since we are looking for the largest possible option, lets try 2-digit numbers formed by the given digits.
The smallest 2-digit number that is divisible by 4 is 36
Then the largest number is:
987436Factor the expression below. A. (x − 6)(x − 6) B. 6(x2 − x + 6) C. (x − 6)(x + 6) D. (x + 6)(x + 6)
Answers
Step-by-step explanation:
X(x+6) - 6(x+6)
X+6x-6x-36
X-36
5 positive integers are arranged in ascending order, as follows:
1,9, 9, 10, X
The mean and the median are equal.
Find X.
Answers
Answer:
x = 16
Step-by-step explanation:
Since the numbers are in ascending order, x is the number with the highest value here.
From the arrangement, we can see that the median (the middle number) is the third number which is 9
The mean is the sum of the numbers divided by their count. So we set up the mean and equate to the median
We have this as;
(1 + 9 + 9 + 10 + x)/5 = 9
29 + x = 5(9)
29 + x = 45
x = 45-29
x = 16
I need help with this, Im never good with these
Answers
Answer:
(a) basketball
(b) hat
(c) stuffed animal
explanation:
I'm not sure if got right but from what i see;
Chances from 1-23 you get a stuffed boi
Chances from 24-54 you get a hat (why)
Chances from 55-100 you get a basketball
Winner 5 got 90, which is between 55-100
Winner 6 got 35, which is between 24-54
winner 8 got a 7, which is between 1-23
Hope I didn't read it wrong
How many marbles do you need to be able to arrange them into the shape of an equilateral triangle with 75 rows
Answers
Answer:
2850
Step-by-step explanation:
1+2+3+4+5+6+7...74+75
just add up all the numbers from 1 to 75
10 ^ (th) term for AP-5,-10,-15,..... is :-(A) -955 (B) 50 (C) -50 (D) 955
Answers
Answer:
C
Step-by-step explanation:
The nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 5 and d = a₂ - a₁ = - 10 - (- 5) = - 10 + 5 = - 5 , then
a₁₀ = - 5 + (9 × - 5) = - 5 - 45 = - 50 → C
Write a recursive rule for the sequence.
x, x, 2x, 3x, 5x, 8x, ...
I know that it adds its last term but I don't know the rule/formula to show that.
Answers
Answer:
f(n)=f(n-1)+f(n-2)
f(1)=1x
f(2)=1x
Step-by-step explanation:
This is the fibonacci sequence with each term times x.
Notice, you are adding the previous two terms to get the third term per consecutive triples of the sequence.
That is:
1x+1x=2x
1x+2x=3x
2x+3x=5x
3x+5x=8x
So since we need the two terms before the third per each consecutive triple in the sequence, our recursive definition must include two terms of the sequence. People normally go with the first two.
f(1)=1x since first term of f is 1x
f(2)=1x since second term of f is 1x
Yes, I'm naming the sequence f.
So I said a third term in a consecutive triple of the sequence is equal to the sum of it's two prior terms. Example, f(3)=f(2)+f(1) and f(4)=f(3)+f(2) and so on...
Note, the term before the nth term is the (n-1)th term and the term before the (n-1)th term is the (n-2)th term. Just like before the 15th term you have the (15-1)th term and before that one you have the (15-2)th term. That example simplified means before the 15th term you have the 14th and then the 13th.
So in general f(n)=f(n-1)+f(n-2).
So the full recursive definition is:
f(n)=f(n-1)+f(n-2)
f(1)=1x
f(2)=1x
Of the four choices given, which two, when written as a system, have a solution of (-4,5)?
х
-1
2
3
5
y
2
-1
-2
-4
2x+y=-3
-2x+y=-3
Х
-1
2.
3
7
0
-3
4
-8
2x+y=-3 and
Х
--1
2
3
5
y
2.
-1
-2
-4
0-2x+y=-3 and
х
-1
2
3
5
у
2.
-1
-2
-4
Answers
Answer:
both choices with 2x+y = -3
Step-by-step explanation:
to have the solution (-4, 5), that point must be on both equations/functions, meaning it must be on either one.
in other words, if the point is not on at least one of the functions, it cannot be a solution for that system.
the given function
2x + y = -3
looks like for the point (-4, 5)
2×-4 + 5 = -3
-8 + 5 = -3
-3 = -3
correct.
but
-2x + y = -3
looks like for (-4, 5)
-2×-4 + 5 = -3
8 + 5 = -3
13 = -3
wrong. the point is not on this function.
as we can therefore rule out 2 of the answer options, the other 2 most be correct.
The two equations which when written as a system has a solution of (-4, 5) is; 2x + y = -3 and 2x + y = -3
Inequalities
The correct equations must have same output with the given one when we place -4 and 5 for x and y respectively.
Now, for 2x + y = -3
At x = -4, and y = 5 we have;
2(-4) + 5 = -3
Same with the right hand side.
For -2x + y = -3;
At x = -4, and y = 5 we have;
-2(-4) + 5 = 13
Not the same with the right hand side.
Thus, the two equations with 2x + y = -3 are correct
Read more about Inequalities at; https://brainly.com/question/24372553
a right triangle has a leg of length 13 and a hypotnuse of length 41 yards. find the length of the other leg (nearest tenth)
Answers
find the circumference of a circular swimming pool with a diameter of 18 feet use 3.4 as an approximation round your answer to the nearest foot
Answers
Answer:
57 feet
Step-by-step explanation:
A circular swimming pool has the shape of a circle
Therefore, find the circumference of a circle
Circumference of a circle = 2πr
Where,
Radius, r = diameter / 2
= 18 feet / 2
= 9 feet
π = 3.14
Circumference of a circle = 2πr
= 2 × 3.14 × 9 feet
= 56.52 feet
Approximately,
57 feet
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answers
Answer:
x ≈ 39.3°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{KL}{KM}[/tex] = [tex]\frac{6.5}{8.4}[/tex] , then
x = [tex]cos^{-1}[/tex] ([tex]\frac{6.5}{8.4}[/tex] ) ≈ 39.3° ( to the nearest tenth )
Step-by-step explanation:
Cos theta =Base/hypotenuse
Base=KL= 6.5
Hypotenuse=KM=8.4
Cos X=
[tex] \frac{6.5}{8.4} \\ [/tex]
X=
[tex] {cos}^{ - 1} \frac{6.5}{8.4} [/tex]
X=39.30 (2decimal)
Brainliest please~
What is the value of x?
Enter your answer in the box.
Answers
3 years later a mother will be 4 times as
old as her son. 3 years ago ,the mother age was two times as old as her son age will be 8 years hence. What are their present ages?
Answers
Answer:
33 and 6 yearsStep-by-step explanation:
Mother's age = mSon's age = s3 years later:
m + 3 = 4(s + 3) ⇒ m = 4s + 12 - 3 = 4s + 93 years ago:
m - 3 = 2(s + 8) ⇒ m = 2s + 18 + 3 = 2s + 21Solve for s by substitution:
4s + 9 = 2s + 212s = 12s = 6Find the value of m:
m = 4*6 + 9 = 33Mother is 33 and son is 6
Helpppp please
Find the volume of this object.
Use 3 for pi
Answers
Answer:
The sphere
[tex]v=\frac{4}{3} \pi r^{3}=\frac{4}{3}*3.14 *2^{3}=\frac{4*3.14*8}{3}=\frac{100.48}{3}=33.493[/tex]
The cylinder
[tex]v=\pi r^{2} h=3.14*(\frac{4}{2} )^{2}*3=3.14*2^{2}*3=9.42*4=37.68[/tex]
Add those two volumes together:
[tex]33.493 + 37.68 = 71.173 in^{3}[/tex]
Tariq wants to make some purple paint.
He mixes blue, red and white paint in the ratio 5:3:2
Tariq needs 60 litres of purple paint.
He gets a discounted price of 60% on the red paint.
Calculate how many litres of red paint he buys at the discounted price.
Answers
Answer:
18 liters
Step-by-step explanation:
Blue : red : White = 5 : 3 : 2
Quantity of Blue paint = 5x
Quantity of Red paint = 3x
Quantity of White paint = 2x
Total paint = 5x + 3x + 2x = 10x
10x = 60 liters
x = 60/10
x = 6
Quantity of red paint = 3x = 3*6 = 18
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities.
The batting order for nine players on a team with 11 people.
Answers
Given:
The batting order for nine players on a team with 11 people.
To find:
The number of possibilities for the given scenario.
Solution:
First, we need to select 9 players from 11 people, it involves combination, i.e. [tex]^{11}C_9[/tex].
Second, we need to arrange the order of 9 selected players, it involves permutation, i.e., [tex]^9P_9[/tex].
The number of possibilities for the given scenario is:
[tex]\text{Possibilities}=^{11}C_9\times ^9P_9[/tex]
[tex]\text{Possibilities}=\dfrac{11!}{(11-9)!9!}\times \dfrac{9!}{(9-9)!}[/tex]
[tex]\text{Possibilities}=\dfrac{11\times 10\times 9!}{2!9!}\times \dfrac{9!}{0!}[/tex]
[tex]\text{Possibilities}=\dfrac{110}{2\times 1}\times \dfrac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{1}[/tex]
[tex]\text{Possibilities}=55\times 362880[/tex]
[tex]\text{Possibilities}=19958400[/tex]
Therefore, the following scenario involves both permutation and combination, and the number of possibilities is 19958400.
Someone help me asap
Answers
Answer:
A
Step-by-step explanation:
There are 270 minutes in 4.5 hrs.
divide that by 45, you get 6.
50*3^6 is 36,450
i'm kinda confused in this question, please help me.
Answers
Answer:
there you go
Step-by-step explanation:
angle DOB is 60 degree.
Answer:
see explanation
Step-by-step explanation:
Given ∠ DOC = 90° then
∠ DOB = 90 - p and
Since AOB is a straight angle , then
4p + 90 - p = 180
3p + 90 = 180 ( subtract 90 from both sides )
3p = 90 ( divide both sides by 3 )
p = 30
4p = 4 × 30 = 120
Then
∠ DOB = 180° - 4p = 180° - 120° = 60°
!!!PLEASE HELP!!!
explain the error
Answers
Answer:
Step-by-step explanation:
x is greater than minus 3. You have everything right but the graph. The arrowhead goes the other way. Around -3 is as small as x gets.
0====0====0====0====0
-3 -2 -1 O 1
O------------------------------->
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answers
Step-by-step explanation:
[tex] \tan(x \degree) = \frac{54}{32} \\ = \frac{3}{4} \\ x \degree = { \tan}^{ - 1} ( \frac{3}{2} ) \\ = 56.3 \degree[/tex]
Can someone help me solve this problem please
Answers
Answer:
In picture
Step-by-step explanation:
Brianliest please~
Which expression is equivalent to −10x−10+2x+9?
Answers
Answer:
-8x - 1
General Formulas and Concepts:
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
-10x - 10 + 2x + 9
Step 2: Simplify
Combine like terms (x): -8x - 10 + 9Combine like term: -8x - 1[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{-10x - 10 + 2x + 9}[/tex]
[tex]\huge\textsf{COMBINE the LIKE TERMS}[/tex]
[tex]\large\textsf{-10x + 2x - 10 + 9}[/tex]
[tex]\large\textsf{-10x + 2x}\\\\\large\textsf{ = \bf -8x}[/tex]
[tex]\large\textsf{-10 + 9}\\\\\large\textsf{ = \bf -1}[/tex]
[tex]\boxed{= \large\textsf{\bf -8x - 1}}\large\checkmark[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf -8x - 1 }}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Determine the domain and range of the function f(x) = 23/1082
O {x| all real numbers} {yly >0}
O {x} all real numbers}; {yl y 2 0}
O {x\ x >0}; {y| all real numbers}
O {x\ x 2 0}; {yl all real numbers}
Answers
Answer:
A
Step-by-step explanation:
The domain is all real numbers and the range is all real numbers greater than zero
The domain is {x| all real numbers} and the range is {y| y > 0}
How to find the domain of a function?
The domain of a function is the set of inputs that we can use in the function. To find it, we initially assume that it is the set of all real numbers, and then remove the problematic values of x.
For example, a problematic point would be a value of x that causes the denominator to be equal to zero.
In this particular case, we can see that the variable is in the exponent, thus it can take any real value and it will not cause any problem, so the domain is the set of all real numbers.
The range is the set of possible outputs. Because in this case, the base is a positive number, the outcomes will only be positive, then the range is given by:
y > 0.
So the correct option is A.
If you want to learn more about range and domain, you can read:
https://brainly.com/question/1770447
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 3 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 67
Answers
Hope this helps- brainliest would be great thanks
What is the radius of the circle: x^2+y^2=4
1. -2
2. -4
3. 4
4. 2
Answers
Answer:
2
Step-by-step explanation:
→ The radius of a circle is square root the 4
2
How do I simplify rational expressions
Answers
Answer:
a rational expression is an expression that has a RATIO in it
look at the word "RATIO"nal
a ratio is just a fraction...
so your question is "how to simplify fractions"
lots of approaches, this is one of them...
PRIME FACTOR the numerator and denominator
[tex]\frac{90}{135}[/tex]
90 = 2 * 3 * 3 * 5
135 = 3 * 3 * 3 * 5
= 2/3 (the two 3's cancel and the 5's cancel)
Step-by-step explanation:
please help so I can watch Coop and Cami ask the world
Answers
Step-by-step explanation:
Simple interest=principal x rate x time÷100
amount borrowed=$500
I=$500x7x6÷100
I=$210
therefore you will pay
amount borrowed+interest
$500+$210
$710
hope this is helpful
Maths assignment
a^3-9a
Answers
Answer:
a³-9a
a³-9a
=a(a+3)(a-3)
Hello please help ASAP!
Answers
Consider a binomial experiment. If the number of trials is increased, what happens to the expected value
Answers
Answer:
The expected value is an expression of the weighted average and can be taken as the (arithmetic) mean
As the number of trials is increased in a binomial experiment, the expected values obtained, in each of the set of trials continuously tend to the theoretical expected value
Step-by-step explanation:
