Describe the transformation of each function compared to its parent function.
I need help please!
Answers
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
Related Questions
CAN SOME ONE HELP?!!!!!!
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Step-by-step explanation:
Problems are in the picture below.
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Answer:
Domain for all of them are from (-infinity, infinity) (ALL REAL NUMBERS)
Range for 7 is (-infinity, 3]
Range for 8 is [-4, infinity)
Range for 9 is (-infinity, 2]
I hope this helps and good luck!
Please solve this, 50 points and BRAINLIEST
-4•6/7•-5/3
Answers
Answer:
5 5/7
Step-by-step explanation:
-4•6/7•-5/3
Put the numbers as fractions
-4/1•6/7•-5/3
Rewriting
-4/1 * 6/3 * -5/7
Simplifying the middle fraction
-4/1 * 2/1 * -5/7
Multiply the first two terms
-8/1 * -5/7
Multiplying
40/7
Changing from an improper fraction to a mixed number
7 goes into 40 5 times with 5 left over
5 5/7
Answer:
40/7
Step-by-step explanation:
hey help me pls:^
brainlisht
Answers
Answer:
84
Step-by-step explanation:
plz mark brainliest
Answer:
the right answer of n is 84
15.5 divided by 33.17
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Answer: 15.5 divided by 33.17 would be 0.46728972
Make sure you put your decimal point
what are the coefficient in this expression? 3y-5x+4
Answers
x+4 over negative 5 =3
Answers
Answer:
x = -4 3/5 or -4.6
Step-by-step explanation:
(x+4)/-5 = 3
Divide -5 from both sides
x + 4 = -3/5
Subtract 4 from both sides
x = -4 3/5
4
The graph below shows the number of cases of candy bars four students sold for a fund rainer and the
total number of candy bars in those cases. How many candy bars are in each case?
Candy Bar Fundraiser Data
Jack
200
100
160
Neil
140
120
Lols
Bars Sold
100
30
60
40
Mike
20
0
8
10
12
Cases Sold
A. 50
B. 30
C. 25
D. 10
Answers
Answer:
the answer is c, 25.
Step-by-step explanation:
This is the graph of Bob's riding his bicycle on Sunday. He started in the morning and after biking for sometime he stopped at McDonald to eat breakfast. How long he stayed at McDonald?
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Answer:
you dont have an image?
Y'all I need help with this !!!
Answers
Answer:
see explanation
Step-by-step explanation:
The opposite angles of an inscribed quadrilateral are supplementary, thus
5x + 20 + 7x - 8 = 180
12x + 12 = 180 ( subtract 12 from both sides )
12x = 168 ( divide both sides by 12 )
x = 14
Thus
∠ RQP = 10x = 10(14) = 140°
∠PSR = 180° - 140° = 40° ( opposite angles are supplementary )
∠ SRQ = 7X - 8 = 7(14) - 8 = 98 - 8 = 90°
∠ QPS = 5x + 20 = 5(14) + 20 = 70 + 20 = 90°
Answer:
what do you need help with
Step-by-step explanation:
Find 62(9) . Express your answer as a fraction in simplest form
Answers
Answer:
558/1
Step-by-step explanation:
Answer:588
Step-by-step explanation:
2 = -6х + 4
what is X?
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This is the right answer because I searched it up
Logan invested $80,000 in an account paying an interest rate of 1\tfrac{1}{4}1 4 1 % compounded monthly. Leah invested $80,000 in an account paying an interest rate of 1\tfrac{7}{8}1 8 7 % compounded continuously. After 17 years, how much more money would Leah have in her account than Logan, to the nearest dollar?
Answers
Step-by-step explanation: 5.6+3.7=8.13-13=0
What is the equation of the linear function?
= -x + 6
A
y = -2x + 3
y=-3x +3
y = ;& + 3
Done
Answers
please help 6th grade math i will give brainliest to answer with worked shown
Answers
Answer:
64
Step-by-step explanation:
She drinks 4 ounces every 30 minutes.
4*2= 8 She drinks 8 ounces in an hour.
8*8=64 She drinks 64 ounces in 8 hours
Which of the following represents a function?
A.(4, 1), (4, 2), (4, 3), (4, 4)
B.(6, 8), (-2, 4), (7, 7), (6, 5)
C.(5, 2), (6, 2), (-5, -2), (-6, -2)
Answers
Because In option A and B the x-values are repeated
Good luck!
While on a trip, you notice that the video screen on the airplane, in addition to showing movies and news, records your altitude (in kilometers) above the ground. As the plane starts its descent (at time x = 0), you record the following data:
Time, x (min.)
Altitude, y (km)
0
12
2
10
4
8
6
6
8
4
10
2
If you were to graph this information, the resulting line would represent a linear function. Using this information from the table and the information on your graph, by how much does the altitude of the plane change for each three-minute change in time during the descent.
a.
The altitude of the plane decreases 2 kilometers for each 3 minutes into the descent.
b.
The altitude of the plane decreases 3 kilometers for each 3 minutes into the descent.
c.
For every 3 minutes, the altitude of the plane increases 3 kilometers.
d.
For every 3 minutes, the altitude of the plane increases 2 kilometers.
Please select the best answer from the choices provided
Answers
Answer:
its c
Step-by-step explanation:
Answer:
Its actually B.
Step-by-step explanation:
what is the answer will be
Answers
Answer:
a. True
Step-by-step explanation:
Any two polygons are similar if their corresponding angles are congruent and the measures of their corresponding sides are proportionalA coat factory had seven coats. If they wanted to put them into two boxes, with t same number of coats in each box, how many extra coats would they have left over?
Answers
Answer:
1
Step-by-step explanation:
7 cannot be split into an even number so take one away and you have 6 which can be split into 3 coats per box, with 1 left over.
solve
a- 7-2 = 4x-5
b- Simplify
3x(x+6)-3x(6-3x)
Answers
Answer:
x=5/4 + 5b/4
b= -1+ 4x/5
The other one is 12x^2
Step-by-step explanation:
i asked my online computer tutoring app thingy
Answer:
1) x=-0.5 and x=-3.41
2) 12x^2
Step-by-step explanation:
a) 7-x^2=4x-5
7-x^2-4x+5=0
-x^2-4x-2=0
Multiply by -1
x^2+4x+2=0
Solve using quadratic formula [tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
we have a=1, b=4, c=2
Putting values to find x
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(4)\pm\sqrt{(4)^2-4(1)(2)}}{2(1)}\\x=\frac{-4\pm\sqrt{16-8}}{2}\\x=\frac{-4\pm\sqrt{8}}{2}\\x=\frac{-4+\sqrt{8}}{2} \ and \ x=\frac{-4-\sqrt{8}}{2}\\x=-0.5 \ and \ x=-3.41[/tex]
So, x=-0.5 and x=-3.41
b) Simplify
[tex]3x(x+6)-3x(6-3x)[/tex]
[tex]3x(x+6)-3x(6-3x)\\=3x^2+18x-18x+9x^2\\=3x^2+9x^2\\=12x^2[/tex]
A man traveled a certain number of miles by automobile and then nine times as far by airplane. His total trip was 600 miles in length. How far did he travel by plane?
x represents miles by: automobile or airplane
9x represents miles by: automobile or airplane
Answers
Answer:
The person traveled 540 miles by plane and 60 miles by automobile.
Step-by-step explanation:
The options are not given to choose from, but this question can be solved as it will only have one answer.
Let the miles traveled by automobile be = x
Then, miles traveled by airplane will be = 9x
Now, the total trip length was = 600 miles
What is the slope of a line with the equation y = 5x + ⅖ ?
Answers
Answer:
The slope would be 5
Step-by-step explanation:
The reason why it would be five is because the slope formula is y=mx+b with m being your slope and b being your y-intercept.
Answer:
slope: 5
Step-by-step explanation:
[tex]y=mx+b[/tex] is the equation used to find the slope of an equation. The slope is ALWAYS the "m" value. So.... in this equation y=5+2/5... the "m" value is 5.... making the slope of the equation 5.
Helppp !!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
Hahhahaha
A plane flies at 350 mph in the direction N 40° E with a wind blowing at 40 mph in the direction S 70° E. What is the plane’s drift angle?
Answers
Answer:
The drift angle is approximately 7.65° towards the East from the plane's heading
Step-by-step explanation:
The speed of the plane = 350 mph
The direction in which the plane flies N 40° E = 50° counterclockwise from the eastern direction
The speed of the wind = 40 mph
The direction of the wind = S 70° E = 20° clockwise from the eastern direction
The component velocities of the plane are;
[tex]R_{Plane}[/tex] = (350 × cos 50)·i + (350 × sin 50)·j
[tex]R_{Wind}[/tex] = (40 + cos 20)·i - (40 × sin 40)·j
The resultant speed of the plane = [tex]R_{Plane}[/tex] + [tex]R_{Wind}[/tex] = 265.915·i +242.404·j
The direction the plane is heading = tan⁻¹(242.404/265.915) ≈ 42.35°
Therefore, the drift angle = Actual Angle - Direction of the plane = 50 - 42.35 ≈ 7.65° towards the East
Answer: A. 5.89
Step-by-step explanation:
edge2020
I need help finding the domain
Answers
Answer:
Range: [-4, 2]
General Formulas and Concepts:
Algebra I
Range is the set of y-values that are outputted by function f(x).Step-by-step explanation:
According to the graph, our y-values span from -4 to 2. Since both points are closed-dot, they are included in the range:
[-4, 2] or -4 ≤ y ≤ 2
Pls help with this question
Answers
Answer:
Opposite sides are congruent
Step-by-step explanation:
First off the equals sign with the wave over it means congruent. It wouldn't be either answer with diagonals because the segments that are congruent are sides of the parallelogram not diagonals. Next even though the congruent sides are parallel by providing the information (AB being congruent to CD and AD bring congruent to CB) opposite are parallel wouldn't be the answer because of what you are given.
Sorry if its wordy I hope this helps : )
please help :( a to d, will give brainliest!!
Answers
Answer:
a) y=4x-3
b) y=-1/2x+4
c) y=-3x+8
d) y=5/3x-1
Step-by-step explanation:
y1-y2/x1-x2
Plug in the numbers and solve.
A business recently upgraded a conference TV they had in their conference room. Originally the TV was 32 inches (across the diagonal) and had a perimeter of 87.16 inches. The new TV is 70 inches across the diagonal. Since the new TV will be recessed in the wall, it will need trim put on the border. What is the perimeter of the new TV? Round your answer to two decimal places.
Answers
Answer:
The perimeter of the new TV is approximately 95.32 inches
Step-by-step explanation:
The diagonal dimension of the original TV = 32 inches
The perimeter of the original TV = 87.16 inches
The diagonal dimension of the new TV = 70 inches
The perimeter of the new TV = 87.16 inches
For the original TV, we have;
Let w be the width of the original TV and l be the length of the original TV, we have;
2·w + 2·l = 87.16
√(w² + l²) = 32
Therefore, we have;
32² = w² + l²
w = (87.16 - 2·l)/2
w = 43.58 - l
32² = l² + (43.58 - l)²
l² + (43.58 - l)² - 32² = 0
l² + 43.58² - 2 × 43.85 × l + l² - 32² = 0
2·l² - 87.16·l + 875.2164 = 0
By the quadratic formula, we have;
l = (87.16 ± √((-87.16)² - 4×2 × 875.2164))/(2 × 2)
Therefore, l = 27.89 inches or l = 15.69
Therefore, w = (87.16 - 2·l)/2 = (87.16 - 2× 27.89)/2 = 15.69
or w = (87.16 - 2× 15.69)/2 = 27.89
Whereby the ratio of the width to the length of the original TV and the new TV are the same, we have;
15.69/27.89
w₂/l₂ for the new TV = 15.69/27.89
∴ w₂ = l₂ × 15.69/27.89
w₂² + l₂² = 70²
∴ (l₂ × 15.69/27.89)² + l₂² = 70²
l₂² × (15.69/27.89)² + l₂² = 70²
l₂²((15.69/27.89)² + 1) = 70²
l₂² = 70²/((15.69/27.89)² + 1) = 3722.04
l₂ = √(3722.04) ≈ 61.0
w₂ = l₂ × 15.69/27.89 = 61 × 15.69/27.89 ≈ 34.32
Therefore;
The perimeter of the new TV = 34.32 + 61 = 95.32 inches.
In this exercise we have to use the knowledge and information given to calculate the perimeter that will correspond to:
The perimeter of the new TV is approximately 95.32 inches
So the data for this exercise is from:
The diagonal dimension of the original TV = 32 inches The perimeter of the original TV = 87.16 inches The diagonal dimension of the new TV = 70 inches The perimeter of the new TV = 87.16 inches
Let w be the width of the original TV and l be the length of the original TV, we have;
[tex]2*(w) + 2*(l) = 87.16\\\sqrt{(w^2 + l^2)} = 32[/tex]
Therefore, we have:
[tex]32^2 = w^2 + l^2\\w = (87.16 - 2*l)/2\\w = 43.58 - l\\32^2 = l^2 + (43.58 - l)^2\\l^2 + (43.58 - l)^2 - 32^2 = 0\\l^2 + 43.58^2 - (2 * 43.85 * l)+ l^2 - 32^2 = 0\\(2)*(l)^2 - 87.16*l + 875.2164 = 0[/tex]
By the quadratic formula, we have;
[tex]l = (87.16 +/- \sqrt{((-87.16)^2 - 4*2 * 875.2164))/(2 * 2)} )[/tex]
Therefore:
[tex]w = (87.16 - (2)*(l))/2 = (87.16 - 2* 27.89)/2 = 15.69\\w = (87.16 - 2* 15.69)/2 = 27.89[/tex]
Whereby the ratio of the width to the length of the original TV and the new TV are the same, we have;
w₂/l₂ for the new TV = [tex]15.69/27.89[/tex]
[tex]w_2 = (l_2)* (15.69/27.89)\\w_2^2 + l_2^2 = 70^2\\(l_2 *15.69/27.89)^2 + l^2_2 = 70^2\\l^2_2 * (15.69/27.89)^2 + l^2_2 = 70^2\\l^2_2((15.69/27.89)^2 + 1) = 70^2\\l^2_2 = 70^2/((15.69/27.89)^2 + 1) = 3722.04\\l_2 = \sqrt{(3722.04)} = 61.0\\w_2= l_2 * 15.69/27.89 = 61 * 15.69/27.89 = 34.32\\[/tex]
The perimeter of the new TV :
[tex]P = 34.32 + 61 = 95.32[/tex]
See more about perimeter at brainly.com/question/6465134
Three students wrote equations on their dry erase boards 1/4=20% 7/10=.70% 13/20=65% Which of these students wrote an equation that is correct?
A. Student one and Student 3
B. Student 2 and Student 3
C. Student 2
D. Student 3
PLEASE HURRY THIS EXAM IS DUE TONIGHT!!!
Answers
Answer:
B
Step-by-step explanation:
Bill purchased x hotdogs and y hamburgers at a baseball game. He spent a total of $10. A hotdog costs 3 dollars and a hamburger costs 4 dollars. Write a linear equation to represent the situation. How many hot dogs and hamburgers did Bill buy?
Answers
Answer:
Bill bought 2 hotdogs and 1 hamburger.
Step-by-step explanation:
If Bill spent $10 total, and a hotdog costs $3 while the hamburger costs $4, then find how many times 3 and 4 go into 10. 3 goes into ten 3 times, and 4 also goes into 10 3 times. but if it was 2 hamburgers and a hotdog, Bill would have spent $11. This is because 4+4=8 and if you add 3 you get 11. But if you do it the other way around, 3+3=6, and if you add 4 to 6 you get 10. Son your answer has to be 2 hotdogs and 1 hamburger, or, X=2 and Y=1.