Given the following function equations, state all of the transformations present on the graph of f(x)

4f(x-1)
-f(2x)
f(-x)+2

Answers

Answer 1

Answer:

See explanation

Step-by-step explanation:

f(x) ==> 4f(x-1)

1. f(x) ==> f(x-1)      Translate the graph 1 unit to the right

2. f(x-1) ==> 4f(x-1) Vertical stretch by a factor of 4

f(x) ==> -f(2x)

1. f(x) ==> f(2x)     Horizontal compression by a factor of 1/2

2. f(2x) ==> -f(2x)    Reflection over the x-axis

f(x) ==> f(-x)+2

1. f(x) ==> f(-x)     Reflection over the y-axis

2. f(-x) ==> f(-x)+2    Translate the graph 2 units up.

Answer 2

Answer:

1)  Translated 1 unit right and stretched vertically by a factor of 4.

2)  Compressed horizontally by a factor of ¹/₂ and reflected in the x-axis.

3)  Reflected in the y-axis and translated 2 units up.

Step-by-step explanation:

Transformations

For a > 0

\(f(x+a) \implies f(x) \: \textsf{translated $a$ units left}\)

\(f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

\(f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}\)

\(\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of $a$} \\& \textsf{If }a > 1 \textsf{ it is stretched by a factor of $a$}\\& \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of $a$}\end{aligned}\)

\(\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of $\dfrac{1}{a}$} \\ & \textsf{If }a > 1 \textsf{ it is compressed by a factor of $\dfrac{1}{a}$}\\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of $\dfrac{1}{a}$}\end{aligned}\)

\(y=-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}\)

\(y=f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}\)

Transformation 1

Given:  

\(4f(x-1)\)

Transformations

\(f(x-1) \implies f(x) \: \textsf{translated}\:1\:\textsf{unit right}\)

\(4\:f(x) \implies f(x) \: \textsf{stretched vertically by a factor of}\: 4\)

Transformation 2

Given:

\(-f(2x)\)

Transformations

\(f(2x) \implies f(x) \: \textsf{ compressed horizontally by a factor of $\dfrac{1}{2}$}\)

\(-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}\)

Transformation 3

Given:

\(f(-x)+2\)

Transformations

\(f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}\)

\(f(x)+2 \implies f(x) \: \textsf{translated}\:2\:\textsf{units up}\)

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Related Questions


What is the cost with sales tax for the phone? Assume that the sales tax is 6%, or 0.06 times the price.

Answers

Answer:

$0.06x

Step-by-step explanation:

Well, you didn’t give us a value for the phone so let’s say the phone is x. . .

Let x=the price of the phone.

x * 0.06=0.06x

Answer:

Step-by-step explanation:

a

Point A is at (3,-8) and point B is at (5,-2.5). What is the midpoint of line segment AB?

Answers

Answer:

\(\displaystyle (4,-5.25)\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)Midpoint Formula: \(\displaystyle (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)

Step-by-step explanation:

Step 1: Define

Point A(3, -8)

Point B(5, -2.5)

Step 2: Find Midpoint

Simply plug in your coordinates into the midpoint formula to find midpoint

Substitute in points [Midpoint Formula]:                                                       \(\displaystyle (\frac{3+5}{2},\frac{-8-2.5}{2})\)[Midpoint] Add/Subtract:                                                                                \(\displaystyle (\frac{8}{2},\frac{-10.5}{2})\)[Midpoint] Divide:                                                                                           \(\displaystyle (4,-5.25)\)

Which is the graph of f(x) =
4(3)?
y
y
7
6
5
5
4
4
3
3
3
2
2
2
-1
1
+
-3 -2 -14
1
2
3
4
5
8
-3 -2 -1
1
2
3
4
5
8
-3 -2 -2
1
2
3
4
5
6
2
2
ܕܝܚ.
جسمة

Which is the graph of f(x) =4(3)?yy765544333222-11+-3 -2 -14123458-3 -2 -1123458-3 -2 -212345622.

Answers

the answer would be the first 1.

The sum of three consecutive odd numbers is 177. Find the number. Step by step please

Answers

X=57 is the required answer and 57 59 and 61 are the required numbers

Answer:

57, 59 and 61

Step-by-step explanation:

Let the first odd number be n The next consecutive odd number is n + 2 and the next one after that is n + 4
(consecutive odd numbers have difference of 2 between them. For example if 7 is the first odd number next one is 9(7+2) and the next one is 11(7+4)

We are given that the sum of the numbers is 177. So we have the following equation:

n + (n + 2) + (n +4) = 177

Simplifying gives

n + n + 2 + n + 4  = 177

Collect like terms:

n + n + n + 2 + 4 = 177
3n + 6 = 177

Subtract 6 from both sides
==> 3n = 177 - 6
==> 3n = 171

Divide by 3 both sides
3n/3 = 171/3

n = 57 and this is the first of the odd numbers

The next odd number is 57+ 2 = 59

and the next one after that is 59 + 2 = 61 (same as 57 + 4)

I will give you brainlist if it is correct. What is the solution to this system of equations?

I will give you brainlist if it is correct. What is the solution to this system of equations?

Answers

Answer:

The correct answer is the last option (-2, 8)

Step-by-step explanation:

You can see that the lines intersect at the point -2, 8.

Hope this helped! :)

Answer:

D.

Step-by-step explanation:

The point (-2,8) is the only given point that is on the two lines in this graph.

If you want to make sure, you can just use a graphing calculator on your laptop/ computer & zoom in on it. Hopefully this helps & gets a brainliest. Thx for giving me time.

Which choice has eukaryotic plant cells?

E. coli
salmonella
muscle
carrot

I know its obvious just checking my work

Answers

Answer: the answer is d carrot

Step-by-step explanation:

i took the test

Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50 a plus 3.75 b equals 2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold?

Answers

Answer:

168 adult tickets were sold

Step-by-step explanation:

Multiply the amount of students by the cost of the student ticket (82 times 3.75) which equals 307.5 . Subtract that from the total amount earned (2071.5) and you get 1764. Divide that by the cost of an adult ticket (10.50), and you'll get the amount of adults who attended, which is 168.

Answer:

168 Adult tickets were sold

Step-by-step explanation:

Vote me brainliest

HELP PLEASE SHOW STEPS I HAVE NO IDEA WHAT TO DO. I HAVE BEEN TRYING TO FIGURE IT OUT BUT I CAN’T.

HELP PLEASE SHOW STEPS I HAVE NO IDEA WHAT TO DO. I HAVE BEEN TRYING TO FIGURE IT OUT BUT I CANT.

Answers

Answer: \(x^{2} +23x+49\)

Step-by-step explanation:

To find the area of the shaded region, you must find the area of the larger rectangle [(x+10)×(2x+5)] and subtract the area of the smaller rectangle [(x+1)×(x+1)] from it.

First, you simplify the larger rectangle's area:

(x+10)×(2x+5) = \(2x^{2} +25x+50\)

Then, simplify the smaller rectangle's area:

(x+1)×(x+1) = \(x^{2} +2x+1\)

Finally, subtract the smaller rectangle's area from the larger rectangle's area:

\((2x^{2} +25x+50) - (x^{2} +2x+1) = x^{2} +23x+49\)

Therefore, the final answer is \(x^{2} +23x+49\).

I hope this helps!

\(\text{Area of rectangle}=\text{lengh}\times\text{width}\\\text{Area of square}=\text{side}^2\)

You just need to find differens between rectangle and square

\(\text{lengh}\times\text{width}-\text{side}^2\\\\(x+10)(2x+5)-(x+1)^2=2x^2+5x+20x+50-x^2-2x-1=x^2+23x+49\)

\(x^2+23x+49\:\text{is our answer}\)

16 families went on a trip which cost them Rs 2,16,352. How much did each
family pay?

Answers

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Billy took 5 tests in his math class. He scored an 89,88,93,90 and 81. What is the variance of his grades in these test? If necessary, round to the nearest hundredth.

Answers

The variance of Billy's grades obtained from his test scores is 15.76

What is variance?

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

The variance is therefore; 78.8/5 = 15.76

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Hercules Films is deciding on the price of the video release of its film Son of Frankenstein. Its marketing people estimate that at a price of p dollars, it can sell a total of
q = 220,000 − 11,000p copies. What price will bring in the greatest revenue?
p = $
Hercules Films is deciding on the price of the video release of its film Bride of the Son of Frankenstein. Marketing estimates that at a price of p dollars, it can sell
q = 240,000 − 12,000p
copies, but each copy costs $4 to make. What price will give the greatest profit?
p = $

Answers

The price of 10 brings the greatest revenue or it is the price at which revenue is maximized.

The revenue is a function of Price multiplied by quantity. The revenue equation for the Hercules films is:

Revenue = Price * Quantity sold

Revenue = p * (220000 - 11000p)

Revenue = 220000p - 11000p²

We need to calculate the price at which revenue is maximized and as price changes, the quantity and revenue are changing. Thus we need to find the derivative of this equation to calculate the value of p.

d/dp = 1 * 220000p° - 2 * 11000p

Where p° = 1

0 = 220000 - 22000p

22000p = 220000

p = 220000 / 22000

p = 10

Thus p = 10 or price is 10 when revenue is mazimized.

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A runner is 7/8 mile from the finish line. If she can travel 3/8 mile per minute, how long will it take her to finish the race?​

Answers

Answer:

2 1/3 minutes

Step-by-step explanation:

Distance:

d = 7/8 mile

Speed:

s = 3/8 mpm

Time:

t = d/st = 7/8 : 3/8 = 7/8 * 8/3 = 7/3 = 2 1/3 min

Answer:

Step-by-step explanation:

A runner is 7/8 mile from the finish line. If she can travel 3/8 mile per minute, how long will it take

pls help me need help

pls help me need help

Answers

Answer:

To find (f/g)(x), we need to divide f(x) by g(x) and simplify the result. Therefore, we have:(f/g)(x) = f(x) / g(x) = (x^2 + 2) / (x + 2)The domain of g(x) is all real numbers except -2, since division by zero is undefined. Therefore, the domain of (f/g)(x) is also all real numbers except -2.To find g(f(x)), we need to substitute f(x) into g(x) and simplify the result. Therefore, we have:g(f(x)) = (f(x))^2 + 2 = (2x^2 + 4x - 6)^2 + 2 = 4x^4 + 16x^3 - 8x^2 + 16x + 34The domain of f(x) is all real numbers, so the domain of g(f(x)) is also all real numbers.To evaluate the specified expressions, we need to substitute the given values of x into the corresponding functions and simplify the results. Therefore, we have:(fg)(2) = f(2) * g(2) = (2^2 + 2) * (2 + 2) = 24(gf)(7) = g(f(7)) = g(27^2 + 47 - 6) = g(92) = 92 + 2 = 94g(√2/7) = (√2/7)^2 + 2 = 2/49 + 2 = 2.0408...f(π/2) = 2(π/2)^2 + 4(π/2) - 6 = π^2 + 4π - 6The domain of g(x) is all real numbers, so g(207) is defined.The domain of f(x) is all real numbers, so f(4-2) and f(4/2) are defined.Therefore, the final answers are:(f/g)(x) = (x^2 + 2) / (x + 2), domain: all real numbers except -2

g(f(x)) = 4x^4 + 16x^3 - 8x^2 + 16x + 34, domain: all real numbers

(fg)(2) = 24

(gf)(7) = 94

g(√2/7) = 2.0408...

f(π/2) = π^2 + 4π - 6

g(207) is defined

f(4-2) and f(4/2) are defined.

1. A bird that was perched atop a 15 foot tree dives down six feet to a branch
below. How far above the ground is the bird's new location?

1. A bird that was perched atop a 15 foot tree dives down six feet to a branchbelow. How far above the

Answers

15 1/2-6= 9.5

The bird would be 9.5 ft from the ground in its new location.

I’m not sure how to answer these questions can someone help pls

Im not sure how to answer these questions can someone help pls

Answers

Answer:

Greatest common factor for 14/16 is 2

Greatest common factor for 3/12 is 3

Greatest common factor for 16/28 is 4

So to simplify 14/16 it is 7/8

To simplify 3/12 it is 1/4

To simplify 16/28 it is 4/7

Step-by-step explanation:

a rock is thrown into a still pond and causes a circular ripple. if the radius of the ripple is increasing at a rate of 4 feet per second, how fast is the circumference changing when the radius is 19 feet

Answers

The rate of change of the circumference is 8π feet per second

Given data ,

The circumference of a circle is given by C = 2πr, where r is the radius. We need to find how fast the circumference is changing when the radius is 19 feet and the rate of increase of the radius is 4 feet per second.

We can start by taking the derivative of both sides of the equation C = 2πr with respect to time t:

dC/dt = 2π(dr/dt)

Here, dC/dt represents the rate of change of the circumference with respect to time, and dr/dt represents the rate of change of the radius with respect to time.

We are given that dr/dt = 4 feet per second, so we can substitute this value into the equation above:

dC/dt = 2π(4) = 8π

So when the radius is 19 feet, the circumference is C = 2π(19) = 38π feet. At this point, the rate of change of the circumference is dC/dt = 8π feet per second.

Hence , when the radius is 19 feet, the circumference is increasing at a rate of 8π feet per second

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if a+b=3, ab=40, and a>b find the value of the following (a+2)(b+2)

Answers

a=1 b=2

1+2=3

1x2=2

hope this answers your question

√3r +5> 1

Please help solve

Answers

The solution to the inequality √3r + 5 > 1 is r > 16/3.

To solve the inequality √3r + 5 > 1, we can follow these steps:

Subtract 5 from both sides of the inequality:

√3r + 5 - 5 > 1 - 5

√3r > -4

Square both sides of the inequality to eliminate the square root:

(√3r)^2 > (-4)^2

3r > 16

Divide both sides of the inequality by 3 to solve for r:

(3r)/3 > 16/3

r > 16/3

Therefore, the solution to the inequality √3r + 5 > 1 is r > 16/3.

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Anthony and six friends went out for steaks and salad. The total cost of the
salad was $42. If each person paid $17, what was the total cost of the steaks?

Answers

Answer:

$77

Step-by-step explanation:

7 people, each person paid 17, 17x7 = 119, salad was 42, 119 - 42 = 77

The total cost is $53

Suppose that y varies directly with x, and y= --27 when x= --3 .
A) write a direction variation equation that relates x and y.
B) Find Y when x= 5

Answers

Answer:

A) y=9x

B) y=45 when x=5

Step-by-step explanation:

Part A

\(y=kx\\-27=k(-3)\\-27=-3k\\9=k\\y=9x\)

Part B

\(y=9(5)\\y=45\)

Find the measure of the arc

Find the measure of the arc

Answers

The answer is kindly 21 (100% correct)

I NEED THIS ASAP!!!!!! The dimensions of triangle B are twice the dimensions of triangle A. The area of triangle B is 112 cm2.

What is the area of triangle A?
A.
56 cm2
B.
63 cm2
C.
126 cm2
D.
28 cm2

Answers

Answer: A. 56 cm2

Step-by-step explanation: 112/2=56 and I divided it because Triangle B is twice of Triangle A.

Solve for x and graph the answer on a number line
2

Answers

The solution to the system of inequalities in interval notation is [-2, 1].

How to solve the system of inequalities?

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Solve for x and graph the answer on a number line2
Solve for x and graph the answer on a number line2

A company is considering introducing two new products. Based on sampling results, the company is expecting a probability of success for Product A of 60% and a probability of success for Product B of 80%. The success of Product A is independent of Product B's success. What is the probability that both Product A and Product B will be successful

Answers

Answer:

I think b

-gxtpuf6a4t sketch see ura5wfyzrud

An account manager for a local software firm believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected: Salesperson Number of Contacts Sales (in millions) 1 14 24 2 12 14 3 20 28 What is the dependent variable

Answers

Answer:

Amount of sales

Step-by-step explanation:

The dependent variable also called the measured or predicted variable is simply the variable obtained due to inputs in of the independent variable. It is the variable which is being measured in an experiment. Here, the test is that the number of sales depends on the number of contact. Here, the number of contacts will has an influence or determines the amount of sales, hence, the number of contacts is the independent variable while the amount of sales is the dependent variable.

What is the area of the figure?

What is the area of the figure?

Answers

Answer: 23.76 sq yds

Step-by-step explanation:

0.5*9.9*4.7=23.76

Area of triangle: 0.5*b*h

Write an equation in slope intercept form for the line that passes through (0,4) and is parallel to y=3x-7

Answers

y=3x+1

explanation
4=3(0)+b
4=3+b
b=1

On Friday, 0.325 of the students in
Keisha's math class were absent. What
percent of the students were absent?
Look at picture for choices!! Quick!!

On Friday, 0.325 of the students inKeisha's math class were absent. Whatpercent of the students were

Answers

It would be c because you move two times the decimal dot to the right, that’s how you get the answer

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Prove: The segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases. Slopes are equal; therefore, segments are parallel

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down,

Answers

The segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases

How to prove: The segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases?

From the figure, we have the following coordinates

B = (a, 0)

D = (d, c)

The midpoint of line segment BD is calculated as

BD = 1/2 * (x1 + x2, y1 + y2)

So, we have

BD = 1/2 * (a + d, 0 + c)

This gives

BD = ((a + d)/2, c/2)

Also, we have:

Lines MN and AB are horizontal lines

This means that they have a slope of 0

i.e.

Slope of AB = Slope of MN = 0

Parallel lines have equal slope

Hence, the segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases

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The sum of three consecutive even integers is 36 . find the smallest of them​

Answers

Answer:

10

Step-by-step explanation:

You can get the three consecutive integers by using algebraic expressions.

Let's solve.

Let x be the smallest even integer.

Let x+2 be the second even integer.

Let x+4 be the largest even integer.

x+x+2+x+4 = 363x+6 = 363x = 36-63x = 30x = \(\frac{30}{3}\)x = 10

Therefore, 10 is the smallest even integer.

x+2 = 10+2 = 12

The second even integer is 12.

x+4 = 10+4 = 14

The largest even integer is 14.

Let's check by adding the three even integers.

10+12+14 = 36

36 = 36

It's correct.

Other Questions
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