Describe the transformation of each function compared to its parent function.
I need help please!

Answers

Answer 1

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!

Answer 2

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

Related Questions

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:

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:

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.

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

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

what are the coefficient in this expression? 3y-5x+4

Answers

3 & 5 are the coefficient ones because they are multiplying a variable

The leading coefficient is -5

2 = -6х + 4
what is X?

Answers

X= I ain’t never seen two pretty best friends, one of them always gotta be ugly

1/3 = x

This is the right answer because I searched it up

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.

Problems are in the picture below.

Answers

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!

What is the equation of the linear function?
= -x + 6
A
y = -2x + 3
y=-3x +3
y = ;& + 3
Done

Answers

Yes it’s the 2 choice

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]

15.5 divided by 33.17

Answers

Answer: 15.5 divided by 33.17 would be 0.46728972

Make sure you put your decimal point

A 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:

Step-by-step explanation:

Its actually B.

Step-by-step explanation:

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

It’s C

Because In option A and B the x-values are repeated

Good luck!

CAN SOME ONE HELP?!!!!!!

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°

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

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

hey help me pls:^
brainlisht

Answers

Answer:

Step-by-step explanation:

plz mark brainliest

Answer:

the right answer of n is 84

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Describe the transformation of each function compared to its parent function. I need help please!

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Describe the transformation of each function compared to its parent function.
I need help please!