The table shows values for two functions. The function g is a transformation of f. How does the graph of g differ from that of f?

I just copied and pasted from my answers. This is A P E X :) Please give brainliest if you like my answer tysm! <3

Step-by-step explanation:

12.3.4

Journal:

Shifting Functions

Journal

Algebra I

Points Possible:

20

Name:

Kathy Drews

Date:

Scenario: Model Rocket Path

Instructions:

•View the video found on page 1 of this Journal activity.

•Using the information provided in the video, answer the questions below.

•Show your work for all calculations.

The Students' Conjectures: Serena and Jack are launching three identical model rockets, each at a different time. Jack says that they need to recalculate the graph each time, but Serena thinks they can just shift the function of the first graph.

1. Complete the table to summarize what you know about each rocket: (3 points: 1 point for each row of the chart)

First rocket

The first rocket is shot from 0 ft off the ground and reaches a vertex of 80 ft in 3.5 seconds before it lands again.  

Second rocket

The second rocket is pretty much the same, but because it was fired 3 seconds after the first rocket, the function is shifted 3 units to the right.  

Third rocket

The third rocket is shot from a height of 20 feet, 6 seconds after the first graph is shot. Because it landed below the point at which it was fired, it took more time to land, making the function appear slightly different, though it was the same.

Evaluate the Conjectures:

2. Do you agree with Serena that you can draw the graphs for the other two rockets by shifting the functions? Or do you think that Jack is correct that you need to recalculate the other two? Explain. (2 points)

I agree with serena. Because the rockets both have identical paths and times for ascent and descent, and ascend an equal distance, the functions can be shifted to show the exact path of each rocket.

Analyzing the Data:

Suppose that the path of the first model rocket follows the equation

h(t) = −6 • (t − 3.7)2 + 82.14,

where t is the time in seconds (after the first rocket is launched), and h(t) is the height of each rocket, in feet.  

3. Compare the equation with the graph of the function. Assume this graph is a transformation from f(t) = –6t2. What does the term –3.7 do to the rocket's graph? What does the value t = 3.7 represent in the science project? (What happens to the rocket?) (2 points)

The value t=3.7 represents the time it took to for the rocket to reach its maximum height.  

4. Again assuming a transformation from f(t) = –6t2, what does the term 82.14 do to the rocket's graph? What does the value h(t) = 82.14 represent in the science project? (What is happening to the rocket?) (2 points)

The value t=82.14 represents the maximum height reached by the rocket.

5. Serena and Jack launch the second rocket 3 seconds after the first one. How is the graph of the second rocket different from the graph of the first rocket? Describe in terms of the vertical and horizontal shift. (2 points)

The graph of the second rocket follows an identical path as the first rocket, but because the timer started when the first rocket was fired, and did not lap when the second rocket was fired, the graph for the two rockets were not in the exact same place. The graph for the second function displays the same path, but it is shifted over 3 places to the right.

6. What is the equation of the second rocket? (2 points)

h(t) = −6 • ((t-3) − 3.7)2 + 82.14

7. They launch the third rocket 3 seconds after the second rocket and from a 20-foot-tall platform. What will the graph of the third rocket look like? Describe in terms of the vertical and horizontal shift. (2 points)

The graph of the third rocket will start 6 seconds after the first, and 3 after the second, so on the graph t(time) will equal 6. H (height) starts at 20, so the function shape is identical to the first two rockets, but the function has shifted 3 places to the right from the graph of the second rocket, and 2.5 up.

8. What is the equation of the third rocket? (2 points)

h(t) = −6 • ((t-6) − 3.7)2 + 82.14+ 2.5

9. Answer the following questions about the three rockets. Refer to the graph of rocket heights and times shown above. (3 points: 1 point for each question)

a. Approximately when is the third rocket launched?

at 6 seconds

b. Approximately when does the first rocket land?

7.25 seconds

c. What is the approximate interval during which all three rockets are in the air?

At approximately 6-7 seconds, all three rockets are in the air.

I just copied and pasted from my answers. This is A P E X :) Please give brainliest if you like my answer tysm! <3

Step-by-step explanation:

12.3.4

Journal:

Shifting Functions

Journal

Algebra I

Points Possible:

20

Name:

Kathy Drews

Date:

Scenario: Model Rocket Path

Instructions:

•View the video found on page 1 of this Journal activity.

•Using the information provided in the video, answer the questions below.

•Show your work for all calculations.

The Students' Conjectures: Serena and Jack are launching three identical model rockets, each at a different time. Jack says that they need to recalculate the graph each time, but Serena thinks they can just shift the function of the first graph.

1. Complete the table to summarize what you know about each rocket: (3 points: 1 point for each row of the chart)

First rocket

The first rocket is shot from 0 ft off the ground and reaches a vertex of 80 ft in 3.5 seconds before it lands again.  

Second rocket

The second rocket is pretty much the same, but because it was fired 3 seconds after the first rocket, the function is shifted 3 units to the right.  

Third rocket

The third rocket is shot from a height of 20 feet, 6 seconds after the first graph is shot. Because it landed below the point at which it was fired, it took more time to land, making the function appear slightly different, though it was the same.

Evaluate the Conjectures:

2. Do you agree with Serena that you can draw the graphs for the other two rockets by shifting the functions? Or do you think that Jack is correct that you need to recalculate the other two? Explain. (2 points)

I agree with serena. Because the rockets both have identical paths and times for ascent and descent, and ascend an equal distance, the functions can be shifted to show the exact path of each rocket.

Analyzing the Data:

Suppose that the path of the first model rocket follows the equation

h(t) = −6 • (t − 3.7)2 + 82.14,

where t is the time in seconds (after the first rocket is launched), and h(t) is the height of each rocket, in feet.  

3. Compare the equation with the graph of the function. Assume this graph is a transformation from f(t) = –6t2. What does the term –3.7 do to the rocket's graph? What does the value t = 3.7 represent in the science project? (What happens to the rocket?) (2 points)

The value t=3.7 represents the time it took to for the rocket to reach its maximum height.  

4. Again assuming a transformation from f(t) = –6t2, what does the term 82.14 do to the rocket's graph? What does the value h(t) = 82.14 represent in the science project? (What is happening to the rocket?) (2 points)

The value t=82.14 represents the maximum height reached by the rocket.

5. Serena and Jack launch the second rocket 3 seconds after the first one. How is the graph of the second rocket different from the graph of the first rocket? Describe in terms of the vertical and horizontal shift. (2 points)

The graph of the second rocket follows an identical path as the first rocket, but because the timer started when the first rocket was fired, and did not lap when the second rocket was fired, the graph for the two rockets were not in the exact same place. The graph for the second function displays the same path, but it is shifted over 3 places to the right.

6. What is the equation of the second rocket? (2 points)

h(t) = −6 • ((t-3) − 3.7)2 + 82.14

7. They launch the third rocket 3 seconds after the second rocket and from a 20-foot-tall platform. What will the graph of the third rocket look like? Describe in terms of the vertical and horizontal shift. (2 points)

The graph of the third rocket will start 6 seconds after the first, and 3 after the second, so on the graph t(time) will equal 6. H (height) starts at 20, so the function shape is identical to the first two rockets, but the function has shifted 3 places to the right from the graph of the second rocket, and 2.5 up.

8. What is the equation of the third rocket? (2 points)

h(t) = −6 • ((t-6) − 3.7)2 + 82.14+ 2.5

9. Answer the following questions about the three rockets. Refer to the graph of rocket heights and times shown above. (3 points: 1 point for each question)

a. Approximately when is the third rocket launched?

at 6 seconds

b. Approximately when does the first rocket land?

7.25 seconds

c. What is the approximate interval during which all three rockets are in the air?

At approximately 6-7 seconds, all three rockets are in the air.

a) - Compressing the P(new) function by a scale of 0.5 about the y axis.

- Moving the P(new) function down by 104 units.

b) The two simplified functions for P(original)

-0.08x² + 10.8x – 200.

-0.16x² + 21.6x – 504.

Step-by-step explanation:

Complete Question

An electronics manufacturer recently created a new version of a popular device. It also created this function to represent the profit, P(x), in tens of thousands of dollars, that the company will earn based on manufacturing x thousand devices: P(x) = -0.16x² + 21.6x – 400.

a. The profit function for the first version of the device was very similar to the profit function for the new version. As a matter of fact, the profit function for the first version is a transformation of the profit function for the new version. For the value x = 40, the original profit function is half the size of the new profit function. Write two function transformations in terms of P(x) that could represent the original profit function.

b. Write the two possible functions from part a in simplified form.

Solution

The equation for the new profit function is

P(x) = -0.16x² + 21.6x – 400

At x = 40, the original profit function is half the size of the new profit function

First, we find the value of the new profit function at x = 40

P(x) = -0.16(40)² + 21.6(40) – 400 = 208

Half of 208 = 0.5 × 208 = 104

P(original at x = 40) = P(new at x = 40) ÷ 2

Since we are told that P(original) is a simple transformation of the P(new)

P(original) = P(new)/2 = (-0.16x² + 21.6x – 400)/2 = -0.08x² + 10.8x – 200 ... (eqn 1)

Or, P(original) = 104

-0.16x² + 21.6x – 400 = 104

P(original) = -0.16x² + 21.6x – 400 - 104 = -0.16x² + 21.6x – 504.

So, the two functions that are simple transformations of P(new) to get P(original) are

-0.08x² + 10.8x – 200

Obtained by compressing the P(new) function by a scale of 0.5 about the y axis.

And

-0.16x² + 21.6x – 504.

Obtained by moving the P(new) function down by 104 units.

Hope this Helps!!!

(1) Train the classifier.

(2) True

(3) Image Pre-processing

(4) Weakly Supervised Learning Algorithm

(5) SIFT (or SURF)

(6) True

(7) True

(8) True

(9) True

(10) Decision Tree Classifier

(11) Softmax

(1) In supervised learning, we have given labels (y) and we have input examples (X) which we need to classify. In Keras or in Scikit-learn, we have a function fit(X, y), which is used to train the classifier. In other words, you have to train the classifier by using the incoming inputs (X) and the labelled outputs (y). Hence, the correct answer is: The fit(X,y) is used to train the classifier.

(2) This statement is primarily talking about the PCA, which stands for "Principal Component Analysis." It is a technique or method used to compress the given data, which is huge, into compact representation, which represents the original data. That representation is the collection of PCs, which are Principal components. PC1 represents the axis that covers the most variation in the data. PC2 represents the axis that covers the variation less than that of in PC1. Likewise, PC3 represents the axis that covers the variation less than that of in PC2, and so on. Therefore, it's true that the variation present in the PCs decrease as we move from the 1st PC to the last one.

(3) Image pre-processing is the phenomenon (or you can say the set of operation) used to improve and enhance the image by targeting the distortions within the image. That distortions are calculated using the neighbouring pixels of the given pixel in an image. Hence, the correct answer is Image pre-processing.

(4) SVM stands for State Vector Machine. It is basically a classifier, which is used to classify different (given) classes with precision. In simple terms, you can say that it is an algorithm, which is partially based on the given labeled data to predict the inputs. In technical terms, we call it weakly supervised learning algorithm. Hence, the correct answer is: Weakly supervised learning algorithm.

(5) There are many algorithms out there to detect the matching regions within two images. SURF (Scale Invariant Feature Transform) and SIFT (Speeded up Robust Feature) are two algorithms that can be used for matching patterns in the given images. Hence, you can choose any one of the two: SURF and SIFT.

(6) Indeed. Higher the accuracy is, better the classifier will be. However, there is a problem of overfitting that occurs when the accuracy of the classifier is way too high. Nevertheless, mostly, the classifier is better when there is higher accuracy. Hence, the correct answer to your question is true.

(7) True. Gradient descent is the process used to tune the parameters of the given neural network in order to decrease the error and increase the accuracy of the classifier. It calculates and fine-tune the parameters from the output to input direction by taking the gradient of the error function (sometimes called the loss function), which is the technique called backpropagation. Hence the correct answer is true.

(8) True. As explained in the part (5), SIFT which is called  scale-invariant feature transform, is an algorithm used to detech the features or the matching regions within given images. Hence, it's true that scale-invariant feature transform can be used to detect and describe local features in images.

(9) True. Clustering is indeed a supervised classification. In clusterning, we use graphs, which contains different data points in the form of clusters, to visualize the data as well. Imagine we have 7 fruits, out of which we know 6 of them, and we have to predict the 7th one. Let's say, 3 are apples and 3 are oranges. The set of apples is one cluster, and the set of oranges is another cluster. Now if we predict the 7th one by using the clustering technique, under the hood, that technique/algorithm will first train the model using the 6 fruits, which are known and then predict the 7th fruit. This kind of technique is a supervised learning, and hence, we can say that clustering is a supervised classification.

(10) In machine learning, Decision Tree Classifier is used to predict the value of the given input based on various known input variables. In this classifier, we can use both numeric and categorical values to get the results. Hence, the correct answer is Decision Tree Classifier.

(11) Softmax is the function which is used to convert the K-dimensional vector into the same shaped vector. The values of the Softmax function lies between 0 and 1, and it is primarily used as an activation function in a classification problems in neural networks (or deep neural networks). Hence, the correct answer is Softmax.

(1) Train the classifier.

(2) True

(3) Image Pre-processing

(4) Weakly Supervised Learning Algorithm

(5) SIFT (or SURF)

(6) True

(7) True

(8) True

(9) True

(10) Decision Tree Classifier

(11) Softmax

(1) In supervised learning, we have given labels (y) and we have input examples (X) which we need to classify. In Keras or in Scikit-learn, we have a function fit(X, y), which is used to train the classifier. In other words, you have to train the classifier by using the incoming inputs (X) and the labelled outputs (y). Hence, the correct answer is: The fit(X,y) is used to train the classifier.

(2) This statement is primarily talking about the PCA, which stands for "Principal Component Analysis." It is a technique or method used to compress the given data, which is huge, into compact representation, which represents the original data. That representation is the collection of PCs, which are Principal components. PC1 represents the axis that covers the most variation in the data. PC2 represents the axis that covers the variation less than that of in PC1. Likewise, PC3 represents the axis that covers the variation less than that of in PC2, and so on. Therefore, it's true that the variation present in the PCs decrease as we move from the 1st PC to the last one.

(3) Image pre-processing is the phenomenon (or you can say the set of operation) used to improve and enhance the image by targeting the distortions within the image. That distortions are calculated using the neighbouring pixels of the given pixel in an image. Hence, the correct answer is Image pre-processing.

(4) SVM stands for State Vector Machine. It is basically a classifier, which is used to classify different (given) classes with precision. In simple terms, you can say that it is an algorithm, which is partially based on the given labeled data to predict the inputs. In technical terms, we call it weakly supervised learning algorithm. Hence, the correct answer is: Weakly supervised learning algorithm.

(5) There are many algorithms out there to detect the matching regions within two images. SURF (Scale Invariant Feature Transform) and SIFT (Speeded up Robust Feature) are two algorithms that can be used for matching patterns in the given images. Hence, you can choose any one of the two: SURF and SIFT.

(6) Indeed. Higher the accuracy is, better the classifier will be. However, there is a problem of overfitting that occurs when the accuracy of the classifier is way too high. Nevertheless, mostly, the classifier is better when there is higher accuracy. Hence, the correct answer to your question is true.

(7) True. Gradient descent is the process used to tune the parameters of the given neural network in order to decrease the error and increase the accuracy of the classifier. It calculates and fine-tune the parameters from the output to input direction by taking the gradient of the error function (sometimes called the loss function), which is the technique called backpropagation. Hence the correct answer is true.

(8) True. As explained in the part (5), SIFT which is called  scale-invariant feature transform, is an algorithm used to detech the features or the matching regions within given images. Hence, it's true that scale-invariant feature transform can be used to detect and describe local features in images.

(9) True. Clustering is indeed a supervised classification. In clusterning, we use graphs, which contains different data points in the form of clusters, to visualize the data as well. Imagine we have 7 fruits, out of which we know 6 of them, and we have to predict the 7th one. Let's say, 3 are apples and 3 are oranges. The set of apples is one cluster, and the set of oranges is another cluster. Now if we predict the 7th one by using the clustering technique, under the hood, that technique/algorithm will first train the model using the 6 fruits, which are known and then predict the 7th fruit. This kind of technique is a supervised learning, and hence, we can say that clustering is a supervised classification.

(10) In machine learning, Decision Tree Classifier is used to predict the value of the given input based on various known input variables. In this classifier, we can use both numeric and categorical values to get the results. Hence, the correct answer is Decision Tree Classifier.

(11) Softmax is the function which is used to convert the K-dimensional vector into the same shaped vector. The values of the Softmax function lies between 0 and 1, and it is primarily used as an activation function in a classification problems in neural networks (or deep neural networks). Hence, the correct answer is Softmax.

The total nom of  code that can be used is equal to 5+3 = 8

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

The solution is given in the image below