Describe the transformation of each function compared to its parent function.
I need help please!
Step-by-step explanation:
In general, for all problems like this, remember the acronym VOHI:
vertical outside, horizontal inside.
1. The parent function here would be [tex]f(x)=x^{2}[/tex]. 4 has been subtracted from the inside, so it is a horizontal change. You might think that it is moving left 4, but it's actually moving right 4. There is a reason for this, but it's not necessary for you to know right now. All you need to remember is that when inside the parentheses, minus means moving right, and plus means moving left. You also have a 9 added to the outside. Vertical outside. This is a vertical change, meaning up and down. This function has been moved right 4 and up 9.
2. First, the parent function is again [tex]f(x)=x^{2}[/tex]. This time, we have [tex]\frac{1}{4}[/tex] on the outside of our function. This means it is a vertical transformation. When the value on the outside is > 1, it is a vertical stretch. When the value is between 0 and 1 (0<a<1), it is a vertical shrink. [tex]\frac{1}{4}[/tex] is between 0 and 1. So, this is a vertical shrink by a factor of [tex]\frac{1}{4}[/tex]. Next, there is a 6 on the inside of the parentheses, meaning a horizontal translation. Remember from problem 1, though, minus=right and plus=left. So, this function has been vertically shrunk by [tex]\frac{1}{4}[/tex] and moved left 6.
3. Again, parent function: [tex]f(x)=x^{2}[/tex]. This one just has [tex]\frac{3}{2}[/tex] on the outside. We know that it's on the outside because otherwise there would be parentheses around both [tex]\frac{3}{2}[/tex] and x. There is not, so it is outside. Outside, vertical. This is a vertical change. Looking back at problem two, when a value is >1, which this is, it is a vertical stretch. So this function has a vertical stretch by [tex]\frac{3}{2}[/tex].
I hope this helps!
Transformation involves changing the position and/or size of a function.
The transformations are:
Translate f(x), 4 units right, and 9 units up.Translate f(x), 4 units left, then compress f(x) vertically by 1/4Vertically stretch f(x) by 3/2[tex]\mathbf{1.\ f(x) = (x - 4)^2 +9}[/tex]
The above function is a square function, and the parent function is:
[tex]\mathbf{f(x) = x^2}[/tex]
First, the function is translated right by 4 units (this is represented by subtracting 4 from x.
i.e.
[tex]\mathbf{f(x) = (x - 4)^2}[/tex]
Next, the function is translated up by 9 units (this is represented by adding 9 to the value of y.
i.e.
[tex]\mathbf{f(x) = (x - 4)^2 + 9}[/tex]
So, the transformation from the parent function is: Translate f(x), 4 units right, and 9 units up.
[tex]\mathbf{2.\ f(x) = \frac 14(x + 4)^2}[/tex]
The above function is a square function, and the parent function is:
[tex]\mathbf{f(x) = x^2}[/tex]
First, the function is translated left by 4 units (this is represented by adding 4 from x.
i.e.
[tex]\mathbf{f(x) = (x + 4)^2}[/tex]
Next, the function is vertically compressed a factor of 1/4 (this is represented by multiplying the function by 1/4
i.e.
[tex]\mathbf{f(x) = \frac 14(x + 4)^2}[/tex]
So, the transformation from the parent function is: Translate f(x), 4 units left, then compress f(x) vertically by 1/4
[tex]\mathbf{3.\ f(x) = \frac 32x^2}[/tex]
The above function is a square function, and the parent function is:
[tex]\mathbf{f(x) = x^2}[/tex]
The function is vertically stretched a factor of 3/2 (this is represented by multiplying the function by 3/2
i.e.
[tex]\mathbf{f(x) = \frac 34 \times x^2}\\[/tex]
[tex]\mathbf{f(x) = \frac 34 \timex x^2}[/tex]
So, the transformation from the parent function is: Vertically stretch f(x) by 3/2
Read more about transformations at:
https://brainly.com/question/13801312
. What part of an hour is your school lunch time?
Answer: It's from 11:02 till 11:35. hbu?
Step-by-step explanation:
I do it online and I be eating 24/7
can someone please please help me? with a reasoning? :(
Answer:
a) 3x + y = -5 & b) y = 1/3 ( 21- 9x )
Step-by-step explanation:
a)
3x + y = -5
y = -3x -5
b)
y = 1/3 ( 21 - 9x)
y = -3x + 7
y = 3x + 2.5
the slop is to be same in the parallel lines. slop means m in ( y = mx + c )
so a) & b) are parallel lines. since their m is -3 .
What is 569 divided by 67.8
Answer: 8.39233038348
Step-by-step explanation:
Answer:
8.39233038348
Step-by-step explanation:
569/67.8=8.39233038348
Plz can someone help me show work for these two problems!!
3x + y = 13
2x - y = -1
Answer:
3x +y = 13
Or, x=13-y/3......eqn(i)
Now putting the value of x
2x - y = - 1
Or, 2(13-y/3) - y = - 1
Or, 26 - 2y /3 - y = -1
Or, 26 - 2y - 3y = - 3
Or, 26 - 5y = - 3
Or, - 5y = - 3 - 26
Or,y = - 39/ (- 5)
Or, y = 7.8~
2. Convert 25.2625° from decimal degrees to degrees-minutes-seconds.
Answer:15
Step-by-step explanation:
Work out the length x.
Х
7.5 cm
16 cm
Answer:
x = 17.7
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]7.5^{2} + 16^{2} = x^{2}[/tex]
[tex]56.25 + 256 = x^{2}[/tex]
[tex]312.25 = x^{2}[/tex]
[tex]\sqrt{312.25} = x[/tex]
[tex]17.7 = x[/tex]
Johny and Rahul divided the benefit of the business in the ratio 7:9. If
Rahul got 4878 rupees as benefit did Johny get?
Answer:
Step-by-step explanation:
7:9 = x:4878
4878/9 times 7
3794 would be your answer
Answer:
3,794 rupees
Step-by-step explanation:
Johny got 7 parts of the benefit while Rahul got 9. This can be represented as a fraction: 7/9
To solve this problem, we can use cross multiplication, where x represents the amount of rupees Johny got:
[tex]\frac{7}{9}[/tex] = [tex]\frac{x}{4878}[/tex]
Multiply 7 by 4,878: 34,146
Multiply 9 by x: 9x
Now the equation looks like this:
9x = 34,146
Divide both sides of the equation by 9 to isolate the x:
9x/9 = 34,146/9
x = 3,794
Johny got 3,794 rupees.
A couple plans to have two children. What is the probability that they have
exactly one boy?
Answer:
1/2
Step-by-step explanation:
Pls answer 4 and 5 for brainly
Number 4 would be: C
And number 5 would be: C
Please Mark as Brainliest!!!
Answer:
Number 4 is c 1/6 and number 5 is also c
Step-by-step explanation:
I just divided 1 and 6 and got 0.1666
and did the same for the other one
pls mark brainliest
which two fractions would make 1/8 plz help
Answer:
1/3 and 5/15
Step-by-step explanation:
whats 11/12+ 3 1/2 ASAP PLEASE
Answer:
4 5/12 or 4.4
Step-by-step explanation:
Answer:
4 5/12 or 53/12 or 4.4
Step-by-step explanation:
hope this helps : )
please help me!
Decrease £40 by 10%
Answer:
36
Step-by-step explanation:
40 * .10 = 4
40-4 = 36
o. How much money is 8% of $15.00?
Answer: 1.2
Step-by-step explanation:
To get 8% you have to do 8/100
that equals .08
Multiply .08 with 15 and it equals 1.2
Answer1.2:
Step-by-step explanation:
Suppose you are constructing a LEGO Technic Land Rover Defender with a total of 2573 pieces. You have already put together 253 pieces. Every minute you add 5 more pieces. Is the relationship linear? How do you know?
Answer: Yes it is
Step-by-step explanation:
A linear relationship simply put, is a relationship between variables that when constructed, forms a straight line. This happens when y changes at a constant rate if x changes by a constant rate as well for instance, 1.
From this question, assume x is minutes and y is the total number of pieces put together. This means that every time x (minutes) increases by 1, y increases by 5 pieces.
The formula would look like this;
y = 5x + 253
This is a formula for a straight line so indeed, this relationship is linear.
Plz help jfkdjdjdjdjd
Answer:
12
Step-by-step explanation:
MARK BRAINLIEST plz
A sociologist polled a random sample of people and asked them their age and annual income. The two-way frequency table below shows the results. Annual income vs. age group Less than $50,000 At least $50,000 Total Ages 44 and under 148 68 216 Ages 45 and above 38 94 132 Total 186 162 348 Which of the following statements is true of those polled? Choose 1 answer: А A person with an annual income of less than $50,000 is more likely to be 45 years old or above. B A person in the 44 and under age group is more likely to to have an annual income of at least $50,000
Answer:
C A person with an annual income of at least \$50{,}000$50,000dollar sign, 50, comma, 000 is more likely to be 454545 years old or above
A person in the 44 and under age group is more likely to have an annual income of at least $50,000 is a correct statement.
We have given that,
A sociologist polled a random sample of people and asked them their age and annual income.
What is the annual income?
annual income is the amount of money you receive during the year into your bank account, before any deductions.
The two-way frequency table below shows the results.
Annual income vs. age group Less than $50,000 At least $50,000
Total Ages 44 and under 148 68 216 Ages 45 and above 38 94 132
Total 186 162 348
A person with an annual income of at least
[tex]=\$50000\\=$50,000dollar[/tex]
Therefore statement b is true.
A person in the 44 and under age group is more likely to have an annual income of at least $50,000.
To learn more about the annual income visit:
https://brainly.com/question/6070671
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Mark bought gifts for his friends, and each gift cost $9. Let y represent the total cost and x represent the number of gifts. Write an equation to represent the proportional relationship between the total cost and the number of gifts he bought.
Answer:
y = 9x
Step-by-step explanation:
You can set up linear equations like this: y = mx + b, where m is the slope or rate, and b is the y-intercept.
9 would be the slope, since he has to pay $9 per gift.
The y-intercept is when x = 0, but if he doesn't buy any gifts, he won't have to pay anything, so b = 0. You don't have to include it since it's 0.
So, it's just y = 9x
Hope that helps! :D
Answer:
easy
Step-by-step explanation:
Evaluate the expression for f = 20.
122 - 2f
A. 82
B. 100
C. 140
D. 2400
SHOW YOUR WORK PLZSSSSS
[tex]\textsf{122 - 2(20)} \\ \mathsf{2(20) = 40} \\ \mathsf{122 - 40 = answer} \\ \uparrow \mathsf{solve \: above \: and \: you \: have \: your \: answer} \\ \mathsf{122 - 40 = \bf82} \\ \\ \boxed{ \mathsf{your \: answer: \boxed{ \bf 82}}} \checkmark[/tex]
Good luck on your assignment and enjoy your day!~
[tex] \dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
Which expression represents the total number of pages Saul has read, where W represents the number of the weeks since he first started reading
Answer:
Y = 50 + 65w
Step-by-step explanation:
HURRYYYYY
Which system of linear inequalities is graphed?
I would have put C. Because if you look at the triangle it makes then do the math with squared numbers then you should get c.
Find the greatest common factor (GCF) for each number set. 56,63
1. 1
2. 6
3. 7
Seema sells two cookers for Rs.2574 each. On one she gains 10% and on the other she loses 10%.Find her gain or loss percent in the whole transaction.
Answer:
18.18%
Step-by-step explanation:
Selling price of one coker = Rs.2574
If she loose 10% on one;
%loss = Cost price - Selliing price/cost price * 100
10 =Cp-2574/Cp * 100
10/100 = Cp-2574/Cp
0.1Cp = Cp-2574
0.1Cp - Cp = -2574
-0.9Cp = -2574
Cp = 2574/0.9
Cp = Rs. 2860
Amount lost = 2860-2574 = Rs. 286
If she gains 10% on the second
%loss =Sp-Cp/Cp * 100
10 = 2574-Cp /Cp * 100
10/100 = 2574-Cp /Cp
0.1Cp = 2574-Cp
1.1Cp = 2574
Cp = 2574/1.1
Cp = Rs. 2340
Amount gained = 2340-2574 = Rs. 234
Total Loss = Amount lost - Amount gained
Total loss = 286 - 234
Total loss = Rs. 52
Total loss % = 52/286 * 100
Total loss % = 5200/286
Total loss % = 18.18%
6/5 divded by (-3/2)
Answer:
Step-by-step explanation:
6/5 ÷ -3/2 = 6/5 x -2/3
-12/15 = - 0.08
Answer:
− 4/5 or −0.8
Step-by-step explanation:
make g the subject of the formula in w = 7 - sqrt g
Answer: g = w² - 14w + 49
[tex]w=7-\sqrt{g}\\\\=> \sqrt{g} =7-w \\\\<=>g=(7-w)^{2}=49-14w+w^{2}[/tex]
Step-by-step explanation:
What is the domain and range please?
Answer:
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. (In grammar school, you probably called the domain the replacement set and the range the solution set.
tell me if I'm correct...im not sure....thanks
....first person gets brainliest
itz 4 maths homework
Answer:
Genuilly I think you’re correct
sorry if it wrong
but, it looks correct and I think it’s correct
(a) (sin A + sin B) (sin A-sin B)
Answer:
Sin^2A-sin^2B
Step-by-step explanation:
(sin A + sin B) (sin A-sin B)
=SinA(sinA-sinB)+SinB(sinA-sinB)
=Sin^2A-sinAsinB+sinBSinA-sin^2B
=Sin^2A-sin^2B
What is the value of x?
Answer:
111
Step-by-step explanation:
You know the angle missing in the triangle is 69 (180-75-36). The angle on a line is 180. So 180-69=111.
OR
Add the two given angles to get 111 as 75+36+(180-x)=180 so if you subract (180-x) it leaves 75+36.
Draw the image 1/2 turn counter clockwise. (Please Help Me at this question will give uh brainliest)!!!
Answer:
Step-by-step explanation:
Without the picture of the arrow I can't give an accurate answer. But, I'll try.
If the arrow is pointing like this -----> half turn counter clockwise should be with it pointing up.
If the arrow is pointing up, it should look like this <-----.
Do you get the idea?