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3 years ago

Determine all the transformations that have happened to f(x) = (x + 4)2 + 2 compared to

Mathematics

1 answer:

Sav [38]3 years ago

3 0

Answer:

Folow the steps to learn what transformations were determined.

Step-by-step explanation:

First we would have to graph the parent function which is f(x) = x^2. Start by finding your x and y values. Find the y values by plugging in the x values into the parent function.

X Y

2 4

1 1

0 0

-1 1

-2 4

Once these points are plotted you can start determining what are the transformations. Find the difference between the parent function and f(x) = (x + 4)^2 + 2 by looking below.

Vertical Shifts:

f(x) + c moves up,

f(x) - c moves down.

Horizontal Shifts:

f(x + c) moves left,

f(x - c) moves right.

The parent function has to be transformed left 4 and up 2. In order to do this shift each point from earlier left 4 and then up 2. In conclusion you will have two functions graphed (parent function and the transformed function).

You might be interested in

The lengths of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 15 days. a. Find the pro

MrMuchimi

Answer:

a. 0.313% (0.003134842261), b. 237.79 days (237.788095878)

Step-by-step explanation:

In this case, the length of pregnancies is a normally distributed variable, with a mean of 266 days, and a standard deviation of 15 days.

A graph showing the distribution, with regions of interest for the answer, is presented below.

<h3>First Part: Find the probability of a pregnancy lasting 307 days or longer.</h3>

To answer the question regarding <em>the probability of a pregnancy lasting 307 days or longer</em>, it is necessary to calculate what the cumulative probability distribution value is at 307 days. By the way, according to the graph below, 307 days are quite far from the population mean (266 days).

Using the function <em>normaldist(266,15).cdf(307)</em>, from free Desmos software on Internet, we find that, at this length (307 days), the sum of all probabilities for all cases at this value is 99.69% (0.996865157739).

Considering that the total area of the curve is 1, then <em>the probability of pregnancy lasting 307 days or longer</em> is 1 - 0.996865157739 or 0.003134842261 (or 0.00313), approximately 0.313%, a very low probabilty.

This probability is showed as the "light blue" region at the right extreme of the graph.

<h3>Second Part: Find the length that separates premature babies from those who are not premature.</h3>

To find the length that separates premature babies from those who are not premature, it is a question about <em>find the days related with the probability of 3% (or 0.03)</em> to find such premature babies. So, it is a question of finding a percentile (or 100-quantiles): given the cumulative normal distribution curve, what is the value (length of pregnancies) that represents this 3%.

Using the function <em>quantile(normaldist(266,15), 0.03)</em>, from free Desmos software on Internet, we obtained a value of 237.79 days (237.788095878) for the length of pregnacies of premature babies. In other words, those babies whose mothers have a length of pregnancy <em>lower</em> than 237.79 days are considered premature, or this is "the length that separates premature babies from those who are not premature".

The area below 237.79 days is the blue shaded region in the graph below, at the left extreme of it.

4 0

3 years ago

Read 2 more answers

when two fractions refer to the same whole, explain why the fraction with a lesser denominator has larger pieces than the fracti

olya-2409 [2.1K]

Answer with explanation:

Consider a Rectangular room, in which four people are residing and another congruent room,in which six people are dwelling.

If Area Occupied by two rooms are same

Then, Area occupied by each person in first room,if there are four person in first room, if represented in terms of fraction is equal to one fourth $\frac{1}{4}=0.25 m^2$ .

And, Area occupied by each person in second room,if there are six person in second room, if represented in terms of fraction is equal to one sixth $\frac{1}{6}=0.17 m^2$ .

So,→→ Area occupied by each person in which four people are residing>Area occupied by each person in which six people are residing.

→→So,Fraction with a lesser denominator has larger pieces(Larger area) than the fraction with a greater denominator smaller pieces(smaller area).

6 0

3 years ago

Read 2 more answers

The range of y = - 32x ^ 2 + 90x + 3

motikmotik

Enter a problem...

Algebra Examples

Popular Problems Algebra Find the Domain and Range y=3/2x^2+4x-9

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The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(

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∞

)

Set-Builder Notation:

{

∈

}

The range is the set of all valid

values. Use the graph to find the range.

Interval Notation:

[

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∞

)

Set-Builder Notation:

{

∣

≥

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}

Determine the domain and range.

Domain:

(

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∞

)

{

∈

}

Range:

[

−

∞

)

{

∣

≥

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}

image of graph

5 0

3 years ago

Read 2 more answers

21 is what percent of 40?

elena-s [515]

1. We assume, that the number 40 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 40, so we can write it down as 100%=40.

4. We know, that x% equals 21 of the output value, so we can write it down as x%=21.

5. Now we have two simple equations:

1) 100%=40

2) x%=21

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=40/21

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 21 is what percent of 40

100%/x%=40/21

(100/x)*x=(40/21)*x - we multiply both sides of the equation by x

100=1.90476190476*x - we divide both sides of the equation by (1.90476190476) to get x

100/1.90476190476=x

52.5=x

x=52.5

now we have:

21 is 52.5% of 40

6 0

3 years ago

Read 2 more answers

What is 996 divide by 12

ladessa [460]

Answer: 83

Step-by-step explanation: If you multiply 83 x 12 you can get 996.

Can I please be marked brainliest, I need them to rank up :( Thank you

3 0

3 years ago